If I'm reading you right and the pedal is high when it's off, and sinks when you start, it sounds like the opposite of a vacuum problem. When the car isn't running, the pedal is firm, but there's no boost. A system that is leaking down or in need of bleeding may feel good when there's no boost. As soon as you get boost, it pushes harder, and whatever is failing shows up. If this is what happens, then your booster is good, and your vacuum is good.
You're going to have to do a little more diagnosis to get better answers, though, because just bottoming out could be many things.
Let's start with what happens when you pump the pedal up, with boost. Does it firm up, or stay down? If it firms up, you might need bleeding or have radically unadjusted rear drums. If it stays down, then something else is the matter, possibly a failed master cylinder, or a mechanical failure in the rear brake that goes beyond mere bad adjustment.
If you pump it up and it seems firm, does it sink slowly under pressure? If it sinks slowly, it's the master cylinder. Often a failing master cylinder will hold at least for a while under a sharp push but sink under gentle pressure.
I assume that if you've bled the system you have also checked your fluid levels and scanned for leaks, so my bet is for either a really bad rear adjustment problem or a bad master cylinder.
While you're at it, it would help to try taking the vehicle on to a nice loose dirt road or driveway, and try locking up the brakes (assuming you have enough brake to drive cautiously to where such a place can be found). Check to see which, if any, wheels have locked up. A failure in one circuit of a dual master cylinder will cause the pedal to go almost to the floor, but then it will engage the un-failed portion at the bottom. So, for example, if you find a little bit of brake at the bottom, and it locks the fronts, you know the problem is in the rear brakes or the rear portion of the MC.
Finally, if the problem appears intermittently while driving, occasionally a soft pedal, and then it recovers, check for bad wheel bearings on the front.