Fantastic frame! Love the color and the chrome fork.
The rear brake rubbing has more to do with the spacing of the cantilever posts than the tire. They're a little narrower than modern canti spacing. The front works because the fork is aftermarket. I can't quite tell if you've tried this from the pictures, but try removing all of the inner spacers from the brake pads to get a little more space in there. Otherwise you'll have to use a different kind of cantilever brake design, those CR720s have great up/down flexibility but don't work well with older touring frames. Anything with a post-mount brake pad should work, as should some modern Shimano cantis like the CX50.