The kind folks at Apple pointed me to a program that re-encodes video into other formats. It’s called VisualHub and it seems to have mostly solved my issue with the funky JVC file format. I thought it was going to take days to re-encode the video into something that Final Cut would recognise; however, after just a few hours of work this morning, all the video is sitting on my external hard drive. I ended up, for simplicity’s sake, saving it all as PAL DV; at this setting, the files were processed faster than real time (on my MacBook Pro).