Why hasn't anybody mentioned converting to 650b???
My "go pretty much anywhere" bike is an old Mondia Super converted to 650x42b. The one thing I had to look for was indented (vs ovalized) chainstays, and even at that there's barely clearance for 42's. The ovalized stays on mid-80's bikes will usually clear 38's. Also, finding brakes to fit can be a challenge. MAFAC Raids are tailor made for 650b, but they've gotten obscenely expensive of late. Like $250 for a pair of calipers. IIRC, Tektro makes dual-pivot calipers that will work, but I've never used those.
So anyway, that's another option for you.