You actualluy do not have a problem. here's why.
There are two things you have to consider here. Footage, where time is based on frame rate, and Compositions, where time is not based on frame rate.
Let's start with Footage.
The interpreted frame rate for footage determines the speed of the playback and therefore the length of the shot. If the footage is 29.97 fps and 10 seconds long the footage will be 10 seconds long in a comp that is 60 fps and it will still be 10 seconds long in a comp that is 24 fps. the only difference is how many frames you will see more than once or how many frames will be missing. Set the frame rate and the time it takes the footage to playback will always be the same.
Unless you do some additional time stretching you will never see the difference between 24 fps footage in a 30 fps comp and 24 fps footage in a 24 fps comp when it plays back at full speed. You can't see the difference when you watch a movie on TV or a movie in a theater. The only time you will see the difference is when you step through a comp or look at a rendered movie one frame or one field at a time and find blended or repeated frames or fields. ALL 24 fps film footage transferred to videotape has repeated and blended fields because that is how it is scanned. 3 fields then 2 then 3 then 2 then 3 then 2, but it's not a problem. The first video cameras that shot 24fps also interlaced the frames and added their own pulldown scheme. Ok, that takes care of footage and frame rate questions. Now let's look at how comps work.
Comps are not footage. Composition time is not dependant on frame rate.
If you have a comp that is 60fps and you trim a layer in that comp at 10 seconds or you set keyframes at 10 seconds and 15 seconds, then you change the frame rate of the comp to 30fps or 24, or 23.976, or even 100fps, the layer will still end at 10 seconds and the keyframes will still be at 10 seconds and 15 seconds. The duration of the comp will not change. The only thing you will notice is that if you zoom into the timeline and look at the out point or the position of the keyframes, they will not precisely line up with the head of a frame. Many folks panic when this happens and waste a bunch of time trying to figure out how to line the keyframes up with the head of each frame. Cuts and keyframes will still start at exactly the same time. They will not happen on the same frame number, but there will be no change in the timing of the cut or the animation. Let me repeat that. There IS NO PROBLEM with keyframes not precisely lining up at the head of the frame so you do not need to worry about animations or in and out points. You will not end up with black frames or mistimed animations.
Nesting a 23.976 comp in a 29.97 comp will cause no timing problems. As long as you do not have Preserve Frame Rate checked in the Advanced composition settings there will be no repeated or blended frames in the main comp because all animations will be based on time.
If you have mismatched the footage frame rate and the composition frame rate then you will see blended or repeated or missing frames. If you accidentally put 30fps footage in a 24 fps comp and you nested that 24 fps comp in a 30 fps comp (did you follow that?) then you will not have any blended frames unless you have selected "Preserve Frame rate when nested" in the composition settings.
So what I am telling you is that you do not have a problem with timing but you may have a problem with blended or missing frames - which you really won't see unless you really start fussing with stretching time. If you want to you can change the frame rate in all the comps to match or you can just not worry about it as long as, you guessed it, you do not have the PFRWN turned on in the Advanced Composition Settings.
Now let's clear up Drop Frame time code. FRAMES and NOT dropped. Nothing is missing. The only difference between non-drop and drop frame timecode is the accuracy of the time display. Non-Drop timecode counts every frame so after a few seconds the time value is no longer accurate. Drop Frame timecode skips some frame numbers, numbers not frames, so the timecode display matches the clock on the wall. When broadcasters had to slow down the tv frame rate from 30 fps to 29.97 to add a couple of scan lines to the signal so we could have Color TV they had to drop some frame numbers so that when the timecode said 30;00:00 the time was 30 minutes and not 30 minutes 1 second and 24 frames.
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