Tested all the files on another workstation which wasn't in use today. Some files were okay on both workstations, some generated errors on both workstations (but not always the same one), some were okay on one workstation but not the other, one introduced a new error message entirely, and another gave two different messages on two different attempts. Gotta love troubleshooting things like this!
Solution turned out to be to repair the Database Manager Server on the file server. Get everybody out of Quickbooks, then go through the Windows Control Panel to the Programs and Features window. Select the database server manager and select Repair rather than Uninstall.
I haven't tested all 29 files, but I have looked at the most critical and they're all working fine (the one that previously kicked me out generated an error once, but worked on a retry; the others worked the first time).
I post the full solution here because the support agent had trouble finding relevant articles; if he hadn't had the same problem with another customer just last week, or I'd ended up talking with someone else, we might still be on the phone.
