I left to run some errands, and when I came back, the restore had apparently completed, and the server had rebooted itself. All the data seems to have made it across, and all the accounts, config data, etc. were preserved as well, as expected. Something that was not preserved, though, were the SQL databases.
I ran the "backup to removable media" from the console menu, which completed successfully (and should have run a pre-backup event before tarring up everything), and I used the restore option on the new installation. I don't know why they weren't preserved, but they most definitely weren't.
Fortunately, since I hadn't overwritten the old drives, I was able to boot from one of them (on a spare computer), run signal-event pre-backup, and copy /home/e-smith/db/mysql/*.dump over to the new server, and then do mysql < whatever.dump for the databases I needed. I also needed to manually add the database users back to mysql (these would probably have come across if I'd imported the mysql.dump file, but I was concerned that it might bring in other data that could hose my system).