I don't post a lot here, but this thread caught my attention. We have a lot of similarities. I have been running ML 13As for 9-10 yrs, having upgraded from ML Aeon-i speakers that I kept for a decade before them. I also listen to rock and electronic music, though as I get older I'm increasingly putting on folk and easier genres. I find it hard to beat the sound from MLs at anything close to the price point, but if I'm being honest I complain of the same issues. I don't think I've heard a system that images as well as my set up (I'm sure there are plenty of these out there, I just haven't personally heard them), but I do feel that my setup is lacking in tonal accuracy and midrange impact and I do get listening fatigue.
Some comments that might help: I have hybrid tube/ss pre-amp and amps, and moving up to these components from my previous solid state pre and class D amps noticeably improved the overly bright presentation and fatigue. It did come at the expense of a higher noise floor however. I have silver coated interconnects, so it was interesting to read some of the comments about cable changes helping others. Might be something to try.
The speakers that were my 2nd favorite when I purchased the 13As were actually the Focal Sopra 2s. The Sopra 3s were noticeably better than the 2s but price and size were a consideration and the MLs I just preferred overall. I listened to Sonus Faber, lower range Wilsons and some others I can't remember and preferred the Focals to them, so take that for what it is worth. I can't speak to long listening session fatigue on them though.
Other than the Focals, the two box speakers in your price range that have most impressed me are the Magico A3s and the YG Acoustics Carmels. The A3s disappeared more than (I think) any box speaker I've heard. I have not heard the Magico S or M ranges, but those aren't in your price range. And the Carmels really had tone and dynamic pluck down with an impressive sense of realism.
I haven't had focused listening sessions with 100s of speaker models, but from what I've heard it is hard to match the scale and staging of big panel speakers with a box, especially one in your price range. The A3 and Carmels are small speakers by comparison, so I wonder if you'd be fully happy with them. Would their big brothers produce the scale and impact you seek without the etch? probably, but not at a comparable cost. I'm kinda on the lookout for something better as well, so it has been an interesting read. Best of luck to us all : )