I am exasperated but relieved to report that, after a whopping 37 days, Iggy FINALLY pooped. He continued eating like clockwork the whole time, so he had 4 or 5 feedings' worth saved up. At around the 30-day mark, his butt was looking very sausage-y so I tried the warm water soak, but all that came of it was some pee and three large urate blobs. It reassured me that his vent wasn't obstructed, but that was about it, and then it was back to the waiting game.
What finally worked? The "darn it, I JUST cleaned that!" technique. Yep, I decided it was time to deep-clean his enclosure anyway, so he went into a little temporary tub while everything was getting washed and wiped. Right as I picked him up to put him back in his fresh and pretty home, I got a funny feeling and eyed his rear end. Sure enough ... his tail started lifting up. I immediately pulled him back towards the temp tub, just barely in time for the tub to catch a powerful JET-STREAM of pee, followed immediately by a poop pile bigger than anything my DOG has ever produced. I don't think there's a moral to this story, but ... hooray?