Think I Got It
OK, I've re-migrated everything and I've managed to adjust the entry ID's on everything so that the URL's will match up. This was a huge pain in the butt…seems like there should be a way for Movable Type to export the entry ID and restore that number upon import. That way any of your PermaLinks won't change even if you migrate to a new machine.
I imagine that the problem won't exist for me anymore, since I've moved to mySQL instead of a Perl database — I can just dump the database and restore it on the new machine, and everything should come along for the ride.