Have you thought of swapping the rings over from the new crankset to the old crankset? An additional plus is that old Sakae crankset almost certainly looks nicer than the new Alivio.

If you're set on using the new crankset, you don't need as much clearance as you have between the chainstays and crankarms, so you might be able to get away with a significantly shorter BB than specced (110 or even 107) as long as there's clearance between the BB shell and the crankarm. A modern 113 mm MTB crankset on a 68x113mm BB often has quite a gap there; does yours?

Old Suntour components are lovely, and it would be great if you could make this work without putting on a new FD.

I wouldn't worry too much about the small differences in chainstay clearance.