Been exchanging twitter messages all afternoon with no luck. They are not willing to do anything other than reprice the whole thing at today's fares. I also asked their Twitter team for a waiver on their own flight, or to reprice in coach and open up award availability (which would have cost an additional ~$1,100). They were unwilling to do the former and said the latter is systemically impossible (which I doubt...)

Going to try one more call to UA tomorrow and even a hail mary over to Swiss, since United has declined to speak to them on my behalf. Thanks for the suggestions, but doesn't look like this one is going to work out. I'm really surprised they're being this unreasonable.