Sync iPhone/iPad with iTunes after library rebuild
In researching solutions, I found this discussion at apple.com in which somebody suggests "damaging" the iTunes library. This lead to a very useful post which discusses how iTunes uses the data it has to recreate what it doesn't have and gives instructions on how to damage (without deleting) the file -- spoiler: erase the data, leave the file.

Fortunately, I had backed up the iTunes files before I recreated the iTunes library.

I copied my backed up files back into the iTunes directory and launched iTunes and rebuilt what it needed to. There were no apps listed in the Apps display though.

When I connected my iPad, iTunes didn't complain about this being an unknown device. As it started to sync, it prompted my to transfer purchases (i.e. the apps on my iPad which didn't show in iTunes) -- but with no hint of having to erase anything. The sync took longer than normal, but everything is there and I can even find the songs which were originally hidden.

iPad is fine, will sync my wife's iPhone tonight.