I will try to reply to a few of your specific points.
In my room I do hear satisfying bass well into the high 20s, which for non-theater content is sufficient for most all music that I listen to. In my use of the LX521 for theater content, I was able to cause extreme (and disturbing) cone movement from exposure to LFE, and of course the speakers did not successfully produce the infrasonic content in any tangible way.
I think that it is widely understood that the match in tonality between the direct and reflected sound is desirable. I see it frequently mentioned on this site with other speakers. There are a couple of points that I think you need to consider though. First, the overall polar area of radiation for a dipole speaker will be less than a typical speaker, and there will be a greater proportion of direct sound for the dipole at the same distance. More on that here: Listening_room (linkwitzlab.com)
Almost any box speaker will send sound to the rear, but in general it is a lowpassed version of the sound that wraps around the box at the baffle transition frequency, generally around a few hundred hertz.
As it turns out, the -6db per octave is a predictable behavior that can be corrected in the filtered signal sent to the amplifier, just at the expense of increased excursion. You are correct that the dipole radiation cancels to different degrees based on wavelength and baffle size, but it does not have to show up in the sound produced once the filters are taken into account.
The Thor was produced when the Orion was still using some Peerless woofers that had limited excursion capability. Linkwitz worked with Seas to produce the L26RO4Y woofers, and once those were in place the Thor became (other than for theater) obsolete. The LX521 can produce bass just fine at a distance, and inside a typical room the bass does not fall off noticeably as you move side to side. It is true that the woofer equalization has in excess of 20db of correction from the high end of its range to the low end, and this compensates for the acoustic cancellation.
Experimentation is wonderful, and I think that if you were to use these speakers you would greatly enjoy the iteration towards a subwoofer implementation that worked for your room. In my experience, though, the 40hz operation is quite satisfactory. If I had a larger theater room that would allow me to use the LX521 I would certainly use them down to 80h or below. Reaching maximum excursion at 40hz would be very loud, and I think that it would take quite a lot of amplifier power.
I do think that you are approaching this with a spirit of curiosity, and so I have expanded my replies. I hope that this has been helpful.
One thing that is complicated that could use more examination is how dipole bass behaves in a room. As I turn the bass modules in my too-small room, the bass does change somewhat. It changes a lot less than you may expect, though, and I think this is likely due to excitation of the room. I hope to move the speakers into a larger more suitable room (again) some day, and perhaps I'll find something new in the bass when I do.
Thanks for a response from someone who actually owns these speakers. The comments I've seen from different users over the years, with both this speaker and its predecessor, is that the deep bass is probably not adequate to satisfy people who want home theater level of bass, but adequate for people who listen to music. I would be in the latter category, however I do sometimes listen to music where the deep bass is an important part of it and it wouldn't sound very satisfying if the deep bass wasn't fully present and accounted for..
In my room I do hear satisfying bass well into the high 20s, which for non-theater content is sufficient for most all music that I listen to. In my use of the LX521 for theater content, I was able to cause extreme (and disturbing) cone movement from exposure to LFE, and of course the speakers did not successfully produce the infrasonic content in any tangible way.
For anyone who isn't thoroughly familiar with the history, the predecessor of this speaker, the Orion, first came into prominence thanks in large part to the praise heaped on it by Peter Aczel, the publisher/editor of The Audio Critic. Criticisms of any speaker design are often based in the understanding of the theoretical distinctions between the given design and more conventional designs. As such, the criticisms of the Orion and the LX521 are generally twofold, and are essentially the same as with any other dipole radiator (or any speaker that approximates a dipole radiator). Some people question whether it is desirable to have so much acoustic energy reflecting from the wall in back of the speaker. Linkwitz obviously believed that this is to be desired, and while he did also mention that the radiation pattern avoided much of the side wall reflections, this benefit seemed sort of secondary, at least less important than the strong desirability of the late reflections from the rear wall, and he emphasized the importance of tonality match of those reflections to the direct wave.
I think that it is widely understood that the match in tonality between the direct and reflected sound is desirable. I see it frequently mentioned on this site with other speakers. There are a couple of points that I think you need to consider though. First, the overall polar area of radiation for a dipole speaker will be less than a typical speaker, and there will be a greater proportion of direct sound for the dipole at the same distance. More on that here: Listening_room (linkwitzlab.com)
Almost any box speaker will send sound to the rear, but in general it is a lowpassed version of the sound that wraps around the box at the baffle transition frequency, generally around a few hundred hertz.
The other criticism that is based in the theoretical understanding of the design approach is with the fact that as frequency moves lower and wavelengths get longer, the cancellation between the front and rear wavefronts increases. I recall that he wrote that the cancellation yields a bass rolloff that increases at -6dB per octave. But I suspect this is fully correct only for a middle region where the wavelength is not a whole lot shorter than the baffle width and not a whole lot wider than the baffle. At frequency high enough to where the tweeters are highly directional, there will not be appreciable cancellation between the front-facing tweeter and the one facing the rear. For upper treble the dipole pattern is achieved merely by virtue of a pair of highly directional tweeters aimed in opposite directions.
As it turns out, the -6db per octave is a predictable behavior that can be corrected in the filtered signal sent to the amplifier, just at the expense of increased excursion. You are correct that the dipole radiation cancels to different degrees based on wavelength and baffle size, but it does not have to show up in the sound produced once the filters are taken into account.
At the other end of the spectrum, I think there must be a point where the wavelength is so great that cancellation between the front and the rear is essentially perfect, such that the effect would not become appreciably worse as the wavelength increases further. The only way I would expect to hear much deep bass from any dipole radiator would be if I were sitting close enough to the speaker that the wavefront coming directly at me, from the two woofers, will be greater in strength than the wavefront that reaches me by propagating around the baffle from the other side. The wavefront that comes from the far side of the baffle has a slightly longer distance to travel, and spreads out more, and is thus slightly weaker than the wavefront that travels a shorter distance to reach me. But when you listen from a distance where the difference between the two distances is minor in relation to the distance, this effect goes away. For any listener a reasonable distance from the speaker and for wavelengths at least a few times greater than the baffle width, it seems likely to me that the wave cancellation would be essentially complete. I would not expect to hear much of anything below 100 Hz unless I were sitting within a few feet of the speaker and directly in front of it, not off to either side. It need not be said that Linkwitz understood this perfectly well. This was the reason that he designed and built the subwoofer, the Thor (if my memory is correct he did the Thor when he was still focused on the Orion, prior to the LX521).
The Thor was produced when the Orion was still using some Peerless woofers that had limited excursion capability. Linkwitz worked with Seas to produce the L26RO4Y woofers, and once those were in place the Thor became (other than for theater) obsolete. The LX521 can produce bass just fine at a distance, and inside a typical room the bass does not fall off noticeably as you move side to side. It is true that the woofer equalization has in excess of 20db of correction from the high end of its range to the low end, and this compensates for the acoustic cancellation.
The reason I have just now written all of this is not to disparage the speaker. I was curious about whether people who own the speaker are satisfied with the deep bass, and the answer from one person suggested an absence of understanding of the unique characteristics of the design. So I thought I would take the time to write a few words about it. For what it's worth I'm a great admirer of Linkwitz partly because of his independent spirit. But I suspect that if I owned either the Orion or the LX521, I would also be an owner of either Thor or some other subwoofer that I thought would do justice to the Orion or LX521. In the Orion/Thor crossover he designed, the handoff point was surprisingly low, around 50 Hz or 60 Hz. I would be inclined to do this differently, choosing a subwoofer known to give a flat response to somewhere up around 200 Hz. For this particular application I would be inclined to use shallow, 1st-order slopes, so that the Orion or LX521 gradually yields to the subwoofer starting where the wavelength is already several times greater than the baffle width, because at this wavelength (about 5.5 feet at 200 Hz), the excursion of the drivers will already be much greater than it will be for the same woofers in a conventional enclosure (greater excursion is needed to make up for the front/rear cancellation and is accomplished by way of equalization).
Experimentation is wonderful, and I think that if you were to use these speakers you would greatly enjoy the iteration towards a subwoofer implementation that worked for your room. In my experience, though, the 40hz operation is quite satisfactory. If I had a larger theater room that would allow me to use the LX521 I would certainly use them down to 80h or below. Reaching maximum excursion at 40hz would be very loud, and I think that it would take quite a lot of amplifier power.
In writing this it was certainly not my intent to step on anyone's toes and I hope that I've not done that. I just got the sense that some of this is not very well understood and I thought that it might be appropriate to sort of rehash some of it. With every unconventional approach to speaker design, there are fundamental questions that cannot be overlooked by anyone who is naturally curious about loudspeakers and acoustics. With the Orion and the LX521, one of these fundamental questions is concerned with dipole speakers generally, and the question is whether, given that the dipole pattern is inherently unachievable in bass frequencies where the wavelength is several times greater than the width of the baffle, it is nevertheless desirable for the radiation pattern in the midrange and treble to be dipole. I don't have an answer to this question. I only know that it is a meaningful question that wouldn't be overlooked by anyone who is fully objective, and that conventional wisdom strongly suggests that any attempt to achieve the dipole pattern in bass, especially deep bass, would very likely yield a compromised result that is neither dipole in radiation pattern nor satisfactory in the more obvious respect.
I do think that you are approaching this with a spirit of curiosity, and so I have expanded my replies. I hope that this has been helpful.
One thing that is complicated that could use more examination is how dipole bass behaves in a room. As I turn the bass modules in my too-small room, the bass does change somewhat. It changes a lot less than you may expect, though, and I think this is likely due to excitation of the room. I hope to move the speakers into a larger more suitable room (again) some day, and perhaps I'll find something new in the bass when I do.