I haven’t had this issue, though the FCP 7 sequences I bring across are simpler than the one you describe.
The only suggestions I have are check the source files for anything unusual, compression, format etc. Premiere is much more forgiving than After Effects when it comes to file formats. No video formats with long GOPs or H.264. ProRes has never given me a problem.
If you’ve used any 3rd party effects in FCP these could also be the culprit.