I have been tinkering over the past few months with my TV headphone setup and agree with all this. I don’t have specific experience with the firestick but my TV has Bluetooth out. My cat would immediately chew a headphone cable if I plugged it into my receiver, so I got a Qudelix to try and use Bluetooth instead. It was okay with the buffer size set to minimum, but the lip sync was off just enough, it bothered me. I’d ultimately suggest avoiding Bluetooth altogether for watching TV, if there’s any way to cable it.

Eventually I got a desktop DAC/amp, plugged in beside the couch, and ran a long cable from the TV around the perimeter of the room (less tantalizing for my cat than the headphone cable clothes lined across the middle of the room). I say “cable” because optical didn’t work, my LG TV has a funky optical output, so I had to use an HDMI audio extractor and run RCA from that.

A simpler solution would have just been to run a really long headphone extension cable from the receiver around the perimeter of the room. It’s like $17, would have saved me a lot of money.