Supposedly I got a hold of someone useful on Monday. Someone called me back Monday night to let me know the part wasn't in stock or whatever and they'd be calling me back in the next day or so. So, that sounded good at least, kinda sounded like they were on the right track, but now it's Wednesday and haven't heard from them.
I'm patiently trudging through the process, but this is the worst support experience of my life.
In case this is useful to anyone, my replacement finally got here, so hang in there. Two weeks, three separate support tickets, and 5 or so calls later. I only just plugged it in over lunch then had to get back to work, but there appears to be no obvious significant issues.