Does that mod drop frames consistently?
If it does then you already know where the dropped frames are. 1 in every 5 frames, 1 in 6, 1in 7 etc, etc.
If you're only getting 4fps at 1920x1080, I think you need to relax your expectations of what you are going to achieve. You're going to have to drop resolution. 1280x720 in raw scales very well to 1920x1080 and is much better then 1080p in Canon H.264.
IMHO, you're going to want at least 15fps to get a final framerate of 23.976. And I still don't think you're going to be satisfied with the final results. But then, some people really like 2 trillion fps interpolated TV's, so your opinion may differ!
If interpolation (with current methods), worked as well as you seem to think it does, more people would be using it. And there is a HUGE difference between interpolating 24 frames into 30 or 60, and interpolating around 10 or 15 frames into 24. 24 fps has sufficient (arguably) captured motion to interpolate, 10 doesn't!