Update:
Dealership called this morning, they've got most everything swapped over from the old engine to the replacement, so they are very nearly finished. They did find that my exhaust manifold was cracked though. Fortunately the warranty company is going to cover the replacement of that as well, and they also agreed to pay for a brand new GM replacement. Apparently they wanted to go with a used one, but the guy at the dealership was able to convince them to pay for a new one. So they are waiting for that to come in from Denver. He thinks that as long as they don't have any other issues they should be finished by Tuesday or Wednesday of next week. All I will have to pay for is my $100 deductible for the warranty, the cost of oil/coolant, and some exhaust manifold bolts. So maybe a couple hundred total or so.
It's sucked being without my H3 for over a month, but I'm glad I'm getting out so darn cheap, and it sounds like I'm going to be in better shape than I was before as well. Hopefully nothing else is wrong, and if it is, the warranty will cover it.