"How can I change the timecode in FCP so I can use the whole clip. Even if the Timecode slips."
DON'T. No no no! If you are wanting to cut offline at lower resolution, then online at a higher one, that proper timecode is ESSENTIAL! Slipping of timecode is unacceptable...period.
Log and capture your footage. Mark in a few seconds after the timecode break, and mark an out a second before the next timecode break. Then log the clip and move on. Yes this is tedious...yes this take time...but let me assure you, doing it this way means that your online will be smooth...and having a smooth online is always a priority.