If you'll consider used look at the Music Reference RM-200. It can be found used for around $2500. Great amp and not "tubey" sounding. The older RM9-Mark II is another excellent choice and can be found for less. Good luck.
Both M60's and MC275 are good recommendations.
I would throw in the Manley Mahi Mahi's for a fun punchy sound and good bang for the buck. They have an Ultralinear and Triode switch and adjustable feedback. Lots O Fun. The power switch in the back caused me some ergonomic problems.
Good ol American Iron w no snow peas.
As someone who owns both Coincident loudspeakers and AtmaSphere amplifiers, my opinion is that despite what is normally said, this isn't the best of matchups. Each of these components is on the more forward, lively, and engaging side, and I often find the combination can be a bit leaner than I prefer. I realize Israel Blume advertises that he uses AtmaSphere amplifiers, but he's also gone out of his way over the past decade to get into the amplifier business.
Personally, my Atma Spheres sound best with my older Fried (A/6 and, especially, Valhalla) loudspeakers, which present a more resistive load than the Coincidents. In fact, I've not heard the Atmas find a better companion. My Coincidents do best with transformer coupled tube amplifiers with more power than what most of their advertising goes towards, such as my Jadis. So, if you're leaning towards Coincident, I'd personally look into brands like AES, Air Tight, Audio Note, BAT, Cary, DeHavilland, Jadis, Manley, Music Reference, Quicksilver, and VAC.
Do consider the AES Super Amp MkII. It is made by Cary and it sold with EL34s or KT90s, but 6550s, KT77s, KT88 and a host of other tubes can be used. The manual clearly outlines biasing values for many tubes and no mods are needed to roll tubes.
What makes this amp so versatile is the use of newly designed transformers. Speakers from 2-32 ohms can be used with one set of speaker binding posts. I am currently using this amp with DIY speakers with Seas Excel drivers like Coincident.
It is quite a remarkable sounding amp. It is not as big hipped sounding as other Cary gear. The bass is very tight and controlled while the over all sound is dynamic, rhythmic, and tuneful. It has a lot in common with SS gear, but with a full-bodied presentation. These observations are made with EL34s. I've haven't rolled tubes because it sound just right and combines the SS and tube sound in one fine amp.
An interesting observation I have noticed is that with Herbies tube dampers on the 2 6SN7 driver tubes the sound becomes even more tight and airy. With the dampness off the tubes it has a fuller sound. I am using a full compliment of EH tubes.
Thanks for the recommendations. It sounds like Music Reference stuff may be the way to go, at least to try out.
Another amp I didn't mention: what about the Audio Research VT100 MKII? Seems like a good value at $2000 used.
Forgot to mention that my preamp is TBD, but likely looking at a Modwright 9.0 Signature.
Try the Rogue 120 or 150 monoblocs. They'll both switch to 1/2 power in triode mode which gives you a whole new dimension to experiment with based on the types of music you're listening to. My personal favorite is the VTL MB-125 which ARE EL-34 based and can also do the 1/2 power triode trick. IMHO EL-34's are the way to go, especially in a VTL amp product... outstanding mids of course, as they're well known for, but they also have tight, punchy bass and a natural, musical top end. Your speakers will either prefer the extra power of the tetrode mode or totally love the triode, but the good news is, you'll actually have the choice. Very reliable too and easy to live with. They run fairly warm and the Rogues run downright hot... but they're all great sounding "tube magic" value for the money. For a completely different sound from the VTL you might consider the CJ Premier 11 (6550's) but the older MV-50, 52 (EL-34 & "old school iteration thereof"), etc will be too tubey for you (as you said you wished to avoid). Good luck.