That's an important detail that would have been nice to have earlier!
I'm a conference meeting. You're a gaming session. Bit of a difference there!
I'm a technical person. I do software dev for my day job...
[Jitsi is] free, open source (referring to the server: you can install it on your own machine if you want, modify it if you want, and connect to that instead of their cloud), and all of the clients run in a web browser...
I haven't looked into it myself, but I wonder how hard it is to make a custom Jitsi server that does what you want. Maybe a fixed number of participants, in fixed locations, showing black when not present. You'd still capture the entire window and crop it to get your custom tiles, but at least they'd be consistent.
Audio would still be limited to what the browser can produce, which is probably a single mix of everyone. But that *might* still be okay, depending on what you're actually doing. As a sound guy, it's like mixing with stems instead of the full multitrack. (Instead of each individual vocal, you have "lead" and "backup", already mixed. And instead of each individual drum mic, you just have "drums". Etc.)
Or, maybe you can have a separate meeting for each participant, in a separate browser window. You'd have a lot of browser windows, but it would keep everything separate and consistent. Maybe that's okay?
Since you're on Windoze, which still gives exclusive access to video sources, you'll probably have to send black to all of those separate browser windows...unless you can modify the server again, to accept your camera once and copy it internally, like OBS does if you use it right...and show black when the other end drops off, instead of mirroring the local feed.
Still probably send black to each individual "meeting", but have a "magic name" that you send your camera to, and that gets copied to the remote end of all the others but not the local end, possibly determined by IP address or something like that...
I dropped Windoze a couple of years ago for other reasons, and use Ubuntu Studio Linux instead. It does allow multiple things to use the same video source, which is REALLY NICE!!!
ubuntustudio.org