I seem to recall that there is a way to ask the town registrar if an item is registered to another player. Am I misremembering? If not - how the heck do I do that?

Hmm that's either not quite right or the registrar in Illistim isn't set up to use it.

Tried:

register item inquire (in case you were being literal)
register longsword inquire
register inquire item
register inquire longsword