Integrated for Martin Logan Electrostatics

Gryphon Diablo 300, very stable into low impedance loads, or wait til october when the new Diablo 333 will be available.

Did you decide on an option? I too have the Martin Logans 13a currently with Krell FPB 300 Power Amp and a Jeff Rowland Capri S2 Pre Amp. Even though the Krell can do 600w into 4ohm and 1200w into 2ohm it gets so hot running the panels I can fry an egg on it! It only ever got warm to slightly hot with previous speakers.

I'm driving my Impression 11As with the Parasound Halo A31 and its a great pairing. The A31 isn't integrated but Parasound makes some great integrateds.

I concur in the Anthem STR, I’m running the Anthem MCA225mk2 to run my Classic 9’s (so it’s powering the panels and woofers), and it’s a great match. 
if you look under the cover of ML’s own line of amplification gear, it’s Anthem inside…which tells you something. 

I was at the florida audio expo three years ago and one room had a mcintosh ma352 driving two Martin Logan speakers.... to me, it was the best sounding system at the show... so there is that.

My suggestion would be stick with Bryston. I am powering my Theos with a 4B3 and they work very well together.  I also powered them with a 3BSST2 and that sounded great as well, good luck. 

Modwright 225 Integrated 

How about the ARC integrated tube amp!

Few DACs in an integrated are rarely beyond very good unless you spend more.  However, a used Aesthetix Mimas with the optional DAC card is the exception. Also their phono card also punches above it’s price point.

ML ESL panels tend to have a difficult impedance curve and will often dip way below 2ohm. You need an amp that can remain stable into 2ohm loads. Class A or Class A/B, doesn’t matter. Power ratings will correspond with the size of your room and how loud you like to listen.

I owned ML Montis (also powered woofers) and drove them with Rogue ST100 at first before I upgraded to Pass XA30.8. Much preferred the 30.8 Class A amp and it drove the ML without skipping a beat. 
Also, keep in mind that the built in phono stages aren’t typically very flexible and you may be limited by those settings to a specific cartridge type or specs.

try MartinLogan Audio Owner Forum; much discussed topic for 11a, 13a, and 15a.  All have a built-in amplifier for low frequencies.

Also, would a "class A" amp sound better for these speakers.  I see that Luxman, Accuphase and a couple of others make class A up to 60W.

Hegel, Luxman or Accuphase all make good integrated’s.  I currently have the Hegel H390, 6K new and I only use it as an integrated. It is also the first integrated I’ve ever had and I am really pleased with the sound.

All the best.

Get the Anthem STR integrated with ARC room correction. ML's are owned by Anthem and that amp should be a perfect match.

https://www.hifi-advice.com/blog/review/digital-reviews/audio-software-reviews/anthem-room-correction-and-martin-logan-renaissance-esl-15a/