Couple of things. First power required is the cube of the speed so to go from 60 to 80 would require that the power increases 2.37 times. Second, there is no replacement for displacement. Change nothing but the the bore (assuming the rest of the system, carb, pipe, etc is up to the task) from 50cc to 80cc and you should see 1.6 times the power. So when you ask who has the fastest Puch, you might want to qualify the displacement.
When I built my land speed racing E50, I replaced the forks with Honda XR80 forks and custom made the swing arm. The stock frame would be dangerous at these speeds. Brakes don't matter at a LSR event but I would want to seriously beef up the stock brakes if you are going fast on the road. For street use, I agree with some of the comments about building a reliable 45mph machine.
Be safe out there.