Have a look at WebTransport to see a future alternative with potential.
For those who are interested, the technical term is signalling (not negotiation), and there are many providers that will help with that (ably.com, pubnub.com, pusher.com), you don't need to build your own infrastructure. WebSockets is also just one option.
Using a SFU/ MCU is almost a requirement for multi person calls, becoming more important for bigger groups.
I had a look at yown.it, I don't know what it does, your description of it is a bit vague. Those problems you mention are not hard to solve: "device signature"? You just set a cookie. Connection dropped? Cookie got you covered. New tab? Cookie got you covered. Refresh? Cookie you got covered.
Other interesting technologies are:
Twilio's network traversal service: https://www.twilio.com/stun-turn
Agora's higher level products (e.g. video call, voice call) https://www.agora.io/en