Besides, didn't Treasure Hunt offer other prizes worth more than $25K?
No.
Also, everybody here is giving completely plausible theories for how the show worked, but am I crazy for saying that Geoff explained how the show when he was alive?
Where is his explanation?
Geoff, to my understanding, was an open book about this stuff on alt.tv.game-shows, and I believe
Chuck Donegan's page about the show cobbles together a lot of Geoff's explanations. Among other things, there was a 15-minute stopdown after a box was picked. Partly to give Geoff a briefing on the skit but also likely for the reason you pointed out--they needed the extra time to set up whatever prize was chosen. On both of Geoff's incarnations, the actual footprint of the prizes needed wasn't as big it would appear. A LOT of the boxes hid checks for smaller amounts (ranging $5,000 to $14,000) and the klunks were usually pretty small, physically speaking--a shopping cart, a pogo stick, a radio. Beyond that...let's say three cars, a couple of boats, a rack of fur coats, some vacation graphics, three rooms of furniture. If every box really was a unique prize/prize package, 30 boxes really needed about as much storage for the prizes as one taping day at
The Price is Right. The 66-box version from 1981 would be tougher, but not impossible. It seems to me that version of the show had a number of prizes represented as photographs mounted on cards.