It seems that the underlying problem is that something is giving the wrong frame rate. It should be 23.976, not 23.98 or 23.975. I think that Final Cut Pro actually uses the correct frame rate of 23.976, even though the UI confusingly rounds up to 23.98 in user-visible controls.
Can you check the movies that are coming out of each step of your pipeline and see where the wrong framerate is being introduced?
What are the exact version numbers of all of the software that you're using here?
So, now all is well. The fix was to use the most/least useful piece of software from Apple: Cinema Tools. Did a batch reconform to "23.98" (or 23.976 in real numbers), and then all was well.
This isn't the first time Cinema Tools has come to the rescue...which Adobe product would I use to do an instant batch reconform like that?
You mean when you Interpret Footage in AE? Or something else?
In this case, I tried interpreting footage to the correct frame rate and still things ended up being 1 frame off. I'd just like to be able to not have to rely on Cinema Tools in the year 2012 to solve this issue
I guess the cool thing that Cinema Tools does (in this case) is that it re-writes the frame rate in the movie file header itself, as opposed to whatever happens in Interpret Footage. Whatever the difference is, it seems to make all the difference.