[Justin Zakowski] “My sequence settings are Frame size: 1280×960, Pixel Aspect Ratio: NTSC CCIR 601/DV (720×480), Compressor: DVCPRO HD 720p60, Quality: 100%, and Render Control: Apple ProRes 422. (Should this be set to “same as Sequence Codec”? Could this be the problem?)”
Where and why did you come up with that? You have different resolutions, different codecs, no way this will work well.
FIrst like we have posted a hundred times, you cannot edit mpeg4 video in FCP, it needs to be transcoded to something like ProRes and all you video should be converted to the same spec. If all your video is SD you need to edit in SD, there is no reason to edit as HD.
Convert everything to 720×480 ProRes, make the sequence match and do from there.