Nick,
This is a highly documented problem with FCP and JVC’s implemetation of HDV (although not in this forum yet).
In a nutshell, every time you start/stop the transport during shooting FCP will create a new clip while digitizing. FCP needs a few seconds to close each file GOP so you lose a few seconds on the next start/stop.
If you truly need a window dub then you will need a decklink or kona card. Using the cards you can digitize the whole tape via component (or HDMI with the decklink HD studio).
FCP may improve the workflow with the next release at NAB in a week.
There are other solutions for digitizing the whole tape but you will not get accurate TC for a rebuild.