Final Cut Pro X :: Dynamically Rotate / Straighten POV Video

I'm not sure exactly what the appropriate terminology is here, but what I'm looking for is an app (not necessarily FCPro) that allows dynamically rotating or "straightening" a video taken with a head POV video camera (i.e. GoPro, et. al.) 

Situation, you are sitting with a head camera strapped to your head (looking appropriately geeky or stupid, whichever), and recording video.  As you do so, your head looks left, right, and due to the environment, you may tilt your head 20-45 degrees to get the view you want to see (NOTE - what I/me/myself want to view with my eyes - camera is "along for the ride" so to speak).  Then you look out "level" again, etc. Now look to the other side, rotating your head again, etc.  (wash, rinse, repeat). 

I'm wanting to take "head tilt" out and keep the video "level", based on some reference/key frames.  Is there a specific app that can do this without destroying too much quality?  Does FCPro even accomplish this? This is NOT a case of stabilization, I need to dynamically rotate the video to make the video appear level/straight, even though the camera was tilted, etc.

Info:
iMac (27-inch, Late 2013), OS X Mavericks (10.9.5), i7 proc, 16GB mem, 3TB Fusion Drive