Framus, Here's how Sloan solved the tuning problem: he attached the nut (the point where the strings attach on ten far side of the banjo head) to a screw mechanism. To fold the banjo, you loosen the screw thereby taking tension off the strings. When you unfold, you retighten the screw and the banjo is, with only minor adjustment, back in tune. The Fold-a-Jo uses nylon strings. I don't think the mechanism would work with metal ones.
Elderly had one on sale recently with photos
showing the mechanism (see the last photo in the series).
I've never seen a Sloan folding tenor banjo, but I don't see why they couldn't make one up on a special order if it isn't a stock item. The nylon strings might be an issue: they work OK for clawhammer/old-timey; I'm not sure how they'd play or sound for the kind of play that is conventional on a tenor. I guess you could take the metal strings off to fold and reattach after folding on a tenor version (the Sloans I've seen are substantial encough to bear metal strings), but that would negate the advantage of the screw mechanism. You'd still be abel to fit the banjo into a backpack or computer bag, though.