I agree with @larsman that a good dedicated headphone amp will likely be significantly better than the one in your Ayre. I’d also encourage you to reach out to Linear Tube Audio and ask about their Velo amp and how it might pair with the 800S and your sound preferences, and if it sounds interesting they offer a return policy so if it doesn’t work out there’s little risk — just another potential option FWIW. LTA headphone amps all get stellar reviews BTW. Best of luck.
Headphones for sound control
I'll be moving to an up-scale life-care facility. The apartments have concrete exterior walls, and I usually listen to small baroque and jazz trios at moderate sound level, But I think headphones may be the way to go when I want to crank it up for large orchestrations like Aida or Mahler's 2nd.
I've been impressed with the sound of my cousin's Sennheiser 800S with his McIntosh headphone amp. I have an Ayer QX-5 Twenty with a headphone driver that Ayer tells me is very good. I suppose the answer is to try the Ayer before buying the McIntosh. I've downsized my rack of Ayer gear to a KEF LS60, but I really like the sound of Ayre electronics. Advice sought.