Brake booster question

In my and Tyler's ongoing SAAB revival we have run into a brake issue.  We replaced all of the flex lines, cleaned up the calipers, replaced the fluid, ect.  After all that when Tyler drove the car around the yard he said the brakes still felt mushy.  Pulled the wheels, hooked a Motive Power bleeder up but no change.  After that we pulled the master cylinder off and found fluid was leaking past the piston, ordered and installed a new on, still the same.  We did discover that pushing the brake pedal multiple times will stall the engine which makes me think the check valve in the booster is bad.  Does that make sense, is there some test I can do to make sure?  The best part is I can't find any rebuilt boosters so I will have to get it rebuilt for almost as much as we paid for the car. 

I know nothing about how boosters work but could you remove the vacuum line to it and cap it off and see what changes?

In reply to EvanB :

Have not driven it like that, but with the ports capped the pedal is hard, like you would expect, and the car doesn't stall.

A vacuum leak in the booster usually makes the brakes hard, not mushy. What do the soft lines look like? How's the adjustment on the handbrake?

Edit: Just remembered that my 2002 had a leaky master way back when. Pumping the brakes would bring the fluid level in the booster up to the level of the line to the intake, and the brake fluid would get sucked into the engine and make it stumble.

Soft lines are new, as is the master.  I could pull a vacuum on the booster with my Mityvac and see if I get any fluid out.