How much work would be required to adapt this to use WebRTC with native H.264 instead of websockets with a javascript-based MPEG1 decoder implementation?
Probably not much. The WebRTC reference implementation[1] by Google and Mozilla is fairly easy to build and embed, assuming your Internet connection can handle a complete checkout of the Chromium repository. Unfortunately it only supports the VP8 codec for video. There is also OpenWebRTC[2] by Ericsson, but it doesn't work on Windows.
Why WebRTC? I think that's more designed for Browser-to-Browser connections. You'd just need to stream an H.264 file using a <video> tag (and use a websocket for the input).
Streaming an unbounded file to a <video> tag can have fairly significant delay compared to webRTC. It's really more designed for one to many situations (such as livestreams or VOD) than one to one low latency.
[1]: http://www.webrtc.org/native-code/development
[2]: http://www.openwebrtc.io/