The import works fine but every time I attempt to quit Final Cut Pro I am unable to do so because of background rendering. This background rendering has been going on for 24 hours at this point.
24 hours seems wrong for what is presumably a < 60 minute tape capture. What does it show if you open the background tasks window? If you quit, it should just warn you that background tasks are running, but not prevent you from closing down.
The extent of FCP analysis and transcoding can be set in preferences. You can tell it whether you want optimized and/or proxy media to be created in addition to your original media, whether to copy to your Events folder, whether to analyze and fix audio and so forth. Depending on what you ask it to do, it could take a while…but again, 24 hours and counting is not normal.
Come to think of it, I don't think you would have the option to create optimized media for a DV import…so that makes the 24 hour render even stranger.