Oh. I just re-read your post about not having a way to place a box that would connect to the TV and I guess the charging stand (that doubles as the transmitter) would cause the same issue. Sorry.
James:
I was looking for wireless headphones a couple of years ago.
Here's my journey.
There's a fair amount of discussion there on the Sennheiser' 175s. I highly recommend them. But I also see they've gone up in price quite a bit. I got them for less than $200 on Amazon back in 2019.