I don't have personal experience with this one, but on paper, it ticks all the boxes.Desktop.
Topping L30 II Review (Headphone Amp)
This is a review, detailed measurements and listening test of Topping L30 II. It was sent to me by the company and costs US $149. It comes in a number of colors. Usability could not be better with positive clicking switches for power/pre and gains. Three gains are provided with the low gain...
www.audiosciencereview.com
This is Topping L30 headphone amp. It is cheap, can handle EDXS, has plenty of power, but just an amp.
For now, you can continue to use your existing DAC. Also leaves you plenty of budget left to get a decent DAC in the future.
From experience, EDXS sings beautifully from 500mW upwards (and that is LOUD!).
For as long as you don't EQ the lower frequencies up (EDXS don't need it anyways), you can EQ the 1.7kHz region up by a few dBs, and not bother with any preamp cut! That way, you don't loose any gain.