Media Source Extensions[1] may be an option. It allows you to feed bytes to a video element, sourcing those bytes from wherever you'd like. There is a demo[2] that literally opens a video and split it in to parts arbitrarily. Chrome, IE, and Safari all have support for MP4 with MSE.

[1] https://en.wikipedia.org/wiki/Media_Source_Extensions [2] http://html5-demos.appspot.com/static/media-source.html