Ed, I have, what I'm guessing, the same setup. When I started bleeding from the back, all was good with a firm pedal, using the conventual way of opening and closing the nipple while pushing and releasing the pedal.
Then I got to the fronts. Not so good. I tried bleeding them the conventual way, but the pedal stayed down when I pushed on it. I was flushing the system, so I pulled the pedal up and repeated until flushed.
To get a firm pedal, I ended up using a syringe that I use for bleeding bicycle brakes. I'm sure any syringe with a bit of clear hose will do. I filled the syringe almost full and attached it to the bleed nipple. Holding the syringe so that it was higher than the caliper, I drew a vacuum on the caliper to draw out whatever air was left then pushed fluid in. I repeated this until there wasn't anymore bubbles coming out. The pedal came up when I pushed fluid back in and I had a firm pedal in the end.
I'm sure one of those bleeders that Gordon came up with might do the trick, but I had to use what I had.
My 2 cents.