Sorry I didn't show up anymore, I was and am still sick. Is the problem now sloved? It sounds as if it is more like "ok, I can live with that compromise". There is Avidemux in which you can shift the audio under the movie, values in 50 and 100 steps (like 200, 300, 350 etc.) are good to start with.
I would write more, but am too sick and haven't got that roxio application, but I imported my VHS tapes with my old Mac and had a problem which I will come to later.
Aside from that: why does it automatically convert?
I had a similar issue with a SATA-PCI-X card and a PowerMac G4 with using iMovieHD-5. After saving the file as "best quality" (which will make a DVC50pro file out of a recorded DV file) and playing the DVC50pro file in Quicktime I had the video ("picture") run away while the audio was normal speed. Saving the file to a Hard Drive on a native port (i.e. the PowerMacs own IDE-connector and not the SATA-PCI card) solved the problem. OR restarting the Mac and reading the file from the SATA drive.
Seeing how heavy and inefficient OS X is written today you get lags with everyday tasks sometime, when the OS is on the 5400rpm HDD and not on an external fast USB3 HDD or SSD. This is actually pretty mean by Apple, to write the OS that stupid, that you need to use a faster HDD or an SSD to let it run with getting the beachball. I don't know, if the HDD speed (5400rpm 2,5" drives) play a role in you App issue.