New brake booster failure?

I replaced the brake booster, which had been losing vacuum, and, even after shimming the rod to properly meet the master cylinder, the pedal travels much farther than it should. The brake engagement is poor. After a few miles of city driving the brakes get quite hot and begin to drag. With the front end in the air (when cool) I made sure that there was no drag in the brakes. I meticulously measured the space between the master's piston and the end of the booster rod and made sure I was shimmed in spec. I tested for pedal travel distance before fluid could be seen surging in the reservoir. Everything seems to check out. I never opened the hydraulic end of the system. What are the odds that the master went bad right when I changed the booster? A bad booster can't make the pedal travel too far and the brake performance poor, right?