Cannot Conform 30fps to 29.97 through Interpret Footage

I have a huge issue of having to sync two different sources: one is a screen recording of a lecture in 30fps and another one is the video recording of the professor giving that lecture.  I think that different frame rates are the reason that the screen recording is progressively going out of sync with the video recording of the talent, although they are synced in the beginning.

Because he is writing formulas on a tablet, it's of utmost importance that I match his actions with the screen recording, as they are seen side by side.

The Modify command doesn't work in any direction for me.  If I want to conform 30fps to 29.97fps, I go Modify>Interpet Footage>Assume This Frame Rate: 29.97fps, hit OK, but nothing happens.  The same is for trying to convert 30fps to 29.97fps.  

If I have to manually keep correcting the footage each time it goes out of sync, I am in for a big trouble.

Any help would be greatly appreciated!