Ha, I'd be glad to post pics when I'm able.
I've already disassembled the bottom bracket, and it was not original--what I pulled out of it was a Shimano sealed-cartridge unit, which I'm really confident was not original on this bike. And when I compare that shimano to a couple of bb spindles I have lying around, one of which came out of a late 1980s trek touring frame, the Shimano is noticeably shorter. So i'm suspicious of it.
Also, I don't know why I hadn't tried this already, but I also have a rear-wheel from a late-80s/early 90s Trek "hybrid," with a 7-speed freewheel. And the 720 frame accepts that wheel, so I guess I now know its 126mm. Still not sure I know if the Suntour Cyclone will cope with a 7-speed, though...?
Also, I've read just enough about chain length to know that with that 28-tooth granny gear on the front, I will be limited as to the biggest sprocket I can have on the back. So that makes me think 7-speed freewheels might be ruled out by that math.