Sample rate conversions should not at all effect timing.
Sounds like you should of synced up the cams and had the audio recorder/workstation ‘slaving’. Or for ease of edit, live switch it with the recorder/workstation slaving to your master record deck and recording a couple of iso cams to cover your mistakes. Keeps you on your toes and lots of fun!
Only thing for the time variance is resync after 4 mins and overlay shots over the cut. you could try ‘fit to fill’ for each song – but may be hard depending what in/out points (drum hits etc) to fit too.
Good luck!
Jon