Fixed the wipers. Bought a replacement "wiper transmission" from an '02 Buick Century for $20 at a local junkyard. They had 3 GP's there, all three of them had the wiper assemblies removed already. Got lucky, and spotted the Century on the way out after I gave up looking. lol
Took about 15 minutes to remove from the Buick, 10 minutes to install everything back into the GTP, then another 5 minutes getting it all adjusted so it stopped in the right place. I didn't have any lithium grease to put on the moving parts before I put the cowl cover back on, so it's a little hesitant when I first turn on the wipers, but I'll get that taken care of soon enough.
Anyone who has been avoiding this repair, do it. It's simple, cheap, and just gets rid of one more problem with the car.