https://www.aliexpress.com/w/wholesale-M-Vave-Wp12.html I picked up a set of these, to be specific. Not quite the same use case as OP.

I wouldnt want any audio going over Bluetooth. The one I bought was 2.4GHz for the low latency so I can game using jt. There is a sound floor, but that can be minimized by broadcasting with volume as close to clipping as possible, without clipping of course. Its not audiophile grade, but it still sounds really good. I can’t tell the difference in 95% of cases.

The wireless transmitter I bought came with two receivers. I hot swap the receiver when it runs out of battery, and I have Velcro on the headset and each receiver so I just slap them on. Works great!