A Shockingly Straightforward Query

I have personally owned a few Carver amplifiers but not his latest tube efforts.  I am also a current Martin Logan (Montis, which was replaced in the line up by your 11As, so very similar) owner.  I think you need to be very careful pairing a tube amplifier with ESL panels.  The impedance mismatch is known to roll off the high end.  When I first got my MLs, I was using Wyred4sound amplification.  I did not particularly care for class D with them.  Just my $.02, but I would be inclined to look elsewhere, especially if you do not have the opportunity to try them first.  The Martin Logans are possibly a little more picky about amplification than other speakers.

Carver warrants tubes for 5 years and stats like the voltage of tube amps, Carver monos is my vote.

I have the Carver Crismon 350 monoblocks.
mac 2600 tube pre with SF Olympica 3s.
Carvers are wonderful. Clear, smooth and detailed. 
I sold my solid state 300x2 two days after getting them. 

Ryan

Since you can't audition either one then the choice is simple: buy the one you can return no questions asked.

If neither one can be returned then the choice is even easier: keep looking.

an10490413
  Bob Carver 350s or the Theta Prometheus. The selected amps will be driving a pair of Martin Logan 11A speakers.

"MartinLogan doesn’t publish impedance, phase-angle or frequency response curves for this speaker. However, they do state that their impedance dips significantly at higher frequencies. This low impedance, (0.6 ohms at 20KHz) with a corresponding increase in phase-angle suggests that amplifiers that aren’t stable into low impedances shouldn’t be used.
MartinLogan’s online FAQs recommend an amplifiers that doubles in wattage between eight and four ohms and again increases its wattage at two ohms. This would seem to eliminate most amplifiers from consideration."

 This tells you what sort of amp to look for, and it's not tubes, if you want to extract the very best out of these speakers.
But if your happy with "a bit of a compromise" the the Carver tubes will be fine.

Cheers George