Got the backhoe back! Man, this dealership is head and shoulders above the rest.
Service manager called yesterday just after noon, says AGCO gave the go-ahead to order whatever was needed, and to do whatever was needed to get the hoe useable in the meantime. He called while the boom was being welded, to give me a heads-up in case I wanted to pick it up that afternoon, which I did. Amazing. That's as good as it gets!
The welder didn't quite get the side plate back to straight, and he definitely put priority on making sure those two pieces were never coming back apart, rather than whether or not it looked pretty. On a piece that's getting replaced anyways, that's perfect. But that is exactly why I went through the hoops to try and get AGCO to replace rather than just repair. There was little-to-no chance that the boom would come out looking good. Does that change how it works? No. But it definitely changes how it would sell, if I ever want to do that. Someone coming in looking at a big chunky weld on the boom arm is going to think I beat the tar out of this machine, no matter what I tell them. And even if they don't walk away, they'd want a significant discount over what the backhoe would otherwise be worth.
From the kick-in-the-gut realization last Friday of what I was looking at, to getting it loaded back on the tractor this morning, the dealership and AGCO really came through on this one. If it hadn't broke on a Friday, and if I hadn't lost another couple days before getting it down there, I'd have been without it for less than 48 hours.
The boom could take six days or six months to come in, no way to know. In the meantime, I'm going to call this situation resolved. I'll post an update once the new one has arrived, and everything is finalized. Thanks to everyone who took the time to look and share your thoughts! And if someone else finds themselves stuck in the same situation, but with a less helpful dealer, I hope this thread gives you the ammo you need to get some results.