Sounds like brake shoes are not adjusted out far enough. I like to use a bottle jack or floor jack to raise one wheel at a time and rotate the tire while listening for friction between brake shoe and drum. Go in and stomp on the brake pedal and rotate again and listen. If it is free-wheelin, you may want to get under and adjust out while tire is rotating till you just begin to hear friction, then back off a couple notches at most. That should get you as close as you can be without draggin the brakes. Do that to all four wheels and it should improve how your pedal feels.
There is supposed to be a litttle nylon cap at end of the pushrod going into the back of the master cylinder. That cap prevents metal to metal wear between the pushrod and the piston. But we are only talkin about less than 1/8 inch play if it is lost. Make sure that cap isn't struck on the piston whn you remove the pushrod.
The '56 car models do have a hi and lo pedal adjustment at the brake pedal arm whereas the '55 models don't have that. Take a look at where your pushrod eyelet is connected at the pedal arm. Changing the position of the pushrod eyelet connection to the arm increases or decreases how much pedal you have before you hit the floor.