Recording cross-platform (H.264?) videos using WebRTC MediaRecorder
You should be able to record to webm/h.264
var options = {mimeType: 'video/webm;codecs=h264'};media_recorder = new MediaRecorder(stream, options);
So you have the right cross platform video format (H.264) in a WebM container.
Now you could try ffmpeg.js and just change the container from WebM to mp4 - coping the H.264 stream - no transcoding (-vcodec copy).
I recorded to webm/h.264 in Chrome but I didn't try re-wrapping it with ffmpeg.js.