Making the best of a bad situation

Oh, there's a ton of free play. I guess the free play can be measured in inches, and the pedal will go almost to the floor with the engine off.

I'll start with readjusting the brakes and see what happens.
Read what @cudamark posted. Free travel is the amount the pedal will move before it ever starts to depress the pushrod. You'll likely have to pull up on the pedal to get a good feel for it. There can also be some between the booster and master cylinder if it has an adjustable rod "there". Some have adjustable rods there and some do not, they just have a solid rod. I would get the free travel out of the pedal side first. That's the adjustment you asked me about earlier.