Triple backed up everything on my Mac (slightly paranoid, based on previous experiences backing everything up to tape, TWICE, verifying both tapes, reinstalling, and then discovering that neither tape was readable).
Dismantled the Mac (Mac mini - the model you need a putty knife to get in to).
Replaced the HDD (not with SSD before you ask, too expensive and I still had the 1TB HDD I bought for this project a couple of years ago).
Put it mostly back together, hampered only slightly by the WiFi antenna lead that fell off and was enjoying its few moments of freedom too much to clip back on.
Booted from an alleged Mavericks install USB stick, which actually worked!
Mild panic when no HDD showed up, and patted myself on the back for not sealing the Mac up yet. Did a quick search and found that I needed to format the HDD first which, after having been done, showed the drive on the list.
Installed Mavericks, went through all the setups for a newly installed OS, and currently installing updates.
This Mac mini is supported under Yosemite, but reports on the interwebs indicate that this old Mac struggles with Yosemite, so I decided to stick with Mavericks. Apparently El Capitan is supported too, but I'd prefer to wait for the first update and reports of performance on this model before taking that leap.
Ahead is still all the apps to install, and all the data to restore.