Reverse center pull cantilever brakes (how to set up and issues)
You can't do this with traditional cantilever brakes, because the straddle wire has to be pulled from above to tension it - attempting to pull it from below would pull into the wheel.

You could pull from the side by using direct pull cantlievers, a.k.a. v-brakes. A Problem Solvers "Travel Agent" could probably be hacked up to work, and a clean implementation could probably be done with one of the no-longer-produced World Class "V-Daptor" adapters, if you could find one.

That said, both of those approaches are probably less elegant than the already-existing pulley method that it sounds like already works on the frame.