Pre-Purchase Annual?

The current owner is concerned about logging another annual just 6 weeks
later should we elect not to purchase

Then have the annual done, but don't have it logged unless you elect to
proceed with the purchase. Heck, it needn't be logged in the logbook anyway
(read the regulation). Have the mechanic log it on a sticker, and then
stick that in the logbook once you own them.

Your seller doesn't sound too sophisticated.

Paul