Thanks for all the replies.
I believe the rear of the frame, which is not a "disc" frame, is actually 130mm.
In terms of fitting 35 mm wide tires on road rims, I have disc-specific 622x13 rims on a different bike now. The
Sheldon Brown tire sizing chart shows that the largest tires that should go on those rims are 25mm (even though I have 28mm tires now). Wouldn't 35mm tires be really pushing it? I'm not even sure they'd seat properly.