There were a few interesting ideas by others in the original comment thread. Mostly on how to compress the sdp so you can get away with just one large QR code without flashing (for example by presharing a dictionary or stripping the sdp down to the bare minimum: https://webrtchacks.com/the-minimum-viable-sdp/).
I lost interest in this approach because it was way more practical to give up on serverless in exchange for only scanning in one direction instead of both ways (e.g., scan a QR code once on mobile to both open the webpage and join a websocket channel, then use it to upgrade to a webrtc connection). It's a neat trick for use cases like AR.js where this is natural to do: https://github.com/jeromeetienne/AR.js
I lost interest in this approach because it was way more practical to give up on serverless in exchange for only scanning in one direction instead of both ways (e.g., scan a QR code once on mobile to both open the webpage and join a websocket channel, then use it to upgrade to a webrtc connection). It's a neat trick for use cases like AR.js where this is natural to do: https://github.com/jeromeetienne/AR.js