Yeah, you're DQ'd from reality insofar as wanting a light mtb with an American BB shell. Otherwise, that's a laudable goal. I think that mtb geometry switched to something quite usable offroad in the 90s, with the standard "NORBA" geometry (short stays, long sloping toptube, steeper angles), but some earlier bikes (Fat Chance comes to mind) looked similar.
Funny you mention Koski. I've always admired their products. The original Pro Cruiser was a groundbreaking frame; it had slack angles of the earliest bikes, but it had the short stays and long TT of later bikes. I'd never heard of any new-production Koski stuff, much less a "Bro Cruiser", so I googled it. Very little info came up at all, but I did find their FB page and some intriguing pics of a twin toptube full-rigid bike with discs and more progressive geometry. Is this the "Bro Cruiser" you speak of?
https://www.facebook.com/KoskiBros....918247729487/1521937328060912/?type=1&theater
Regardless, that's an impressive frame....
It'd be easy enough to put some headtube reducers in the Transition bike to run a threaded fork, but the transition has super long stays anyway. The Transition guys claim they aped the Worksman INB's geometry as a basis for their "Klunker"s dimensions and angles. Interesting. I gotta say, although I like the look of a threaded 1" headset/quill set-up, 1.125" threadless is definitely a more robust design for offroading. And, the "mid" bb shell is pretty sweet, too... I run some tubular bmx-type 3 pieces on some klunks anyway, and the "mid" set-up is essentially an American BB except that it obviates the need for press-in cups. You can run any 3-piece set up for an American shell, and you might even be able to run a 1piece if you took a BB220SB's hardware and got creative with some quasi-standard cartridge bearings. But, the Transition's geometry is a deal-breaker for you anyway; it has the same geometry you're trying to avoid, plus it uses newer standards that you dislike. And, it ain't exactly lightweight. You'd be better off with a Worksman from Chuckz....
I think you could probably find a mid-90s full rigid bike for fairly cheap, and cut out the shell and weld in an American shell yourself.... or, have someone else do it for you. By then, a lot of the bikes were already 1.125", but you could use reducers or just look for a Bridgestone MB-_ series bike, which will have 1" threaded set-ups. If it were me, though, I'd just live with the BSC-style BB shell and the vast array of stiff, light, versatile cranks that work with it....