I’ve never heard of someone doing something like this before, but it sounds like it could have some pretty cool downstream applications (thinking Bluetooth speakers)
With your setup would it be possible to pair your headphones to your phone (iPhone in my case) and be able to pass audio from different computers to a central one that my phone could then relay to my headphones?
I often walk around my house/yard while listening to something playing on my laptop/desktop. And if I get too far from the source, it breaks the Bluetooth connection. So I usually end up having to drag my laptop around the yard with me. A much nicer solution would be to have my phone on my person, and use the wifi to keep connected to my “audio source” without needing proximity to the actual pc playing the sound.