78buckshot - My personal experience with the same circumstances a couple years ago on my 3100 was a failed master cylinder. Under single push steady pressure the cup didn't seal against the cylinder wall, allowing fluid to bypass the piston and cup.
I could rapidly pump it and gain some pressure, but then holding would result in the same pedal drop to the floor. A little different than yours, but thinking it's master cylinder related.
I vote for a master cylinder rebuild or replacement.
