suggestion for a SS class AB amp that sounds like a class A ... if such a thing exists

Your Sudgen is a respectable amp, and have worked on some Altec related custom designs with a few friends, they can be transparent with great crossover parts inside, once upgraded.  While I hate to open this can of worms, what sort of source and cabling are you running for ICs and speaker wire?  

Are you already running silver plated interconnect or speaker cabling,  sometimes a simple move from OFC to OCC crystal copper cabling can add transparency.  OCC can be really open and smooth too.  Maybe some other areas to check too while considering replacing your amp, fwiw.  

Benchmark.

I listen mostly to digital sources... a 16 feet long standard USB cable goes from my computer to the Benchmark DAC1, and another 12 feet long cable goes from the DAC to the Sugden... I used a standard USB cable because the guy at Benchmark told me there was no need for a better one. I don’t know much about the second cable but it looks like a good one. As for my speakers wire, they are OFC Audioquest... I used to have a much better cross over made with oil condenser and other military grade parts, but I had to sell it in order to buy my actual Altec... The sound was better but I also had a different amp...

I was curious about my Atoll A/B integrated and I wrote to Atoll about this question. They responded right away. They said,

"The IN200 works in Class A up to about 40W under 8 Ohm. The switch to Class AB is quite slow."

Possibly of interest.

The Benchmark will be by far and away the least class A-sounding, so delete immediately from your list.

But are you looking for an integrated or a power amp?

Alongside the Ayre integrated, you could look at the Belles Aria.