We had to do the re-install. All the big stuff is done, but I'm still working on all the little things (redirected folders, recreating staff shortcuts, deleting Bing off the face of the Earth, etc). It's slow-going, mostly because I'm taking fastidious notes along the way for future reference, since I had little to look at this time around.
On the plus side, unless his bill is out of control, the new hardware IT guy is a keeper. And a HUGE shout out to Nick at AC Support, who made sure we had all the files we needed backed up before the restore, then got back in afterwards to re-install AC and the data. Still knocking on wood, but as far as I can see we didn't lose anything.
Thanks a bunch for all the suggestions. Keep your fingers crossed for me that whatever happened the first time around doesn't decide to repeat itself.