By shifting to the right do you mean the right pad touches or the left?

I don't know how your cables are routed but on older top tube routed cables you can usually move the cable through the eyelets or clamps a little bit and the friction will keep them where you moved them to. The movement/cable location changes the pressure exerted on the rear brake. If you mess with that and see how it changes things you should be able to figure it out.