Combine 360˚ video with 2D footage? (not PiP)

Hello,

Currently dealing with an issue regarding 360˚ video. Would like to combine it with normal shots without warping those shots to the equirectangular projection. This is not the same as inserting 2D footage in to a 360˚ video (I am aware of how to do that) but needs to be solved so that a viewer can be watching a normal video and then at certain points take control of the 360˚ footage before going back to 2D. 

Any suggestions? Would be greatly appreciated.

Thank you.