Hi Matthew, I am not sure if this will work and don’t have time to test it, but this sounds like a job for the lesser known ‘Time Remapping’ feature to me:

Render the 16FPS part out as a video at 24FPS with the time remapping as above and then 16 frames of the original should last 24 frames in the newly created video, so you should (theoretically, if I didn’t make any mistakes) be able to combine that with the 24FPS part.
Again, I didn’t test it and I do not guarantee success, but it might work…(I hope it does!)