After several long and incoherent conversations with the ticket people, I am confirmed on a flight out tonight (instead of the tomorrow morning flight they wanted to put me on.)
I just got the confirmed itinerary that I requested, and I am not only confirmed on the new flight, but apparently on the flight that's leaving, oh, right now, and that I was moved off of.
I *then* got a receipt with price information for the new flight (it's about the same, if not exactly the same, as the original price).
So I thought about calling back to confirm that a) I am not actually confirmed on two flights to Other Side, and b) that I am not expected to pay for Booking # 2.
But then I thought, "You know? I've spent a long time on hold today."
And then, "What if they tell me that I need to pay for the new flight? Of course I won't do it. I'll yell at them and risk not making it out of here at all."
So I concluded, "Far better to just show up at the airport and then, if they somehow try to make me pay (and how would they do that?), refuse."
Finally, "I'm surely just being hyper conscientious here, and there's no chance they're actually going to try to bill me for a rebooked flight when they're the ones who screwed me over in the first place."
Because the airline industry is fuzzy like that.