Is this a bad brake booster?

My brakes are REALLY spongy.

I swapped the lines to stainless braided, adjusted the rear breaks, flushed the lines (well, maybe not full true flush, but I pushed the black nasty fluid out and have nice pale yellow fluid to all four corners), and then bled the system.

Get in the car after doing all that, and the pedal feels GOOD. Nice and firm. Right up until I fire the car up, and then the pedal turns to total mush again.

When I get on the brakes, they're good up top, but if I keep pushing, the pedal will go to the floor. A quick brake pump firms things up for the top of the next press.

I figure it's a bad brake booster, I don't think a leak would act like that, would it?

Sounds like a master cylinder to me.

If the sponginess is new, it's air in the lines. Possibly a bad master cylinder.

If it was there before, I'd bet it's air in the lines, a stuck brake caliper slider, or a bad master cylinder. Try super gently applying the brakes and see if you can ever-so-slowly sink the pedal right to the floor with very little effort = bad master.

Wouldn't a bad master always be mushy, though? I was leaning towards the booster as the pedal is firm after a bleeding, but turns to mush when the engine is fired up (it's an auto, so my foot's on the brake pedal when I hit the ignition and it hold up right to the point where the engine fires, then it just sinks).

Oh, and the spongyness has always been there, but it got MUCH worse after a track day. I figured I boiled the fluid, which is why I was flushing it in the first place.