4K Apple TV, dual Bluetooth headphones, and audio drops

I've been using a 4K Apple TV with two Beats Flex for a couple of years now and it worked great: stable, no audio dropouts, and hardly any issues at all. Then I swapped out one of the Beats Flex headphones and started using a pair of Beats Fit Pros. Everything worked fine for a couple of months, then tvOS 16 came out and the problems started.

15+ times in an hour long viewing session on both pairs of headphones we'll get dropped audio. Sometimes it's a split second, sometimes it's a full second.

Things I've tried:

1) Rebooting the Apple TV (currently running tvOS 16.2 (20K362)

2) Removing the Bluetooth pairing and re-pairing both sets of headphones

3) Turning off Bluetooth on my nearby iPad and phone

4) I bought a second pair of Beats Fit Pro and swapped out the pair I was using in this room, same issue

None of these things have worked. It's incredibly irritating thing to start happening after pure bliss for two years. I'm out of ideas so I thought I'd ask here. I try not to conflate correlation and causation, but it does seem to be linked to tvOS 16 in some way; the problems started almost immediately after it was installed, and no other variables changed that I'm aware of.

The one thing I haven't tried is using both pairs of Beats Fit Pro in this setup, but I doubt the results would be any different.