If it was a blown booster the pedal would be hard and the engine would run like crap as if it had a massive vacuum leak.
I think you are on the right track with the spreader bar/adjuster star wheel. They can be installed backwards and they are different threads from each side, one side is regular thread the other is revererse(left) thread.
What sounds like is happening is your brakes are backing off, the first pedal application takes up the slack and the second then actually applies the brakes. This is often seen with disc brakes that have badly warped rotors that push the piston back into the caliper as they turn.
Did you properly adjust the rear brakes after installing the shoes? You have to manually adjust ups the star wheel to take up the slack after servicing, once its close the mechanism will keep it adjusted after that., provided you don't get it full of mud.
A severely warped drum or axleshaft could also be pushing the shoe back, not as likely though.