How does my MF A308 compare to modern integrated amps in the $3000-$6000 range?

no not if its working properly

Thanks. I’m happy with the sq, but I have no frame of reference regarding other options.

I'm with @jjss49 

Mostly what you'll find out there will only be different, not unequivocally better or worse.  Unless there's a particular aspect of your sound that's lacking and needs addressed (and is easily attributable to amplification), I wouldn't start a new search. 

If you do start wandering, I'd try to start sampling totally different typologies (e.g., a full tube integrated, a class d integrated, an otl) rather than just sticking with other class a/b amps. You'll learn more that way.

And as always, amp to speaker matching is an essential and hard to fully predict challenge.

op did not disclose, but with his good amp, if he is trying to improve overall sq, he should look at source or speakers (assuming room setup is done properly) for areas of substantial improvement for more $ spent... that is where there will likely be more leverage