Whether in the shop, or in the pits, this is all that I have ever used to bleed brakes:
Brake Bleeder Bottle You will need two.
I wonder if heat is causing the pistons to warp in these old calipers?
Before you go pulling the caliper apart, open the bleeder screw and see if you can't press the piston back in with a C-clamp. If it's the piston seizing in the bore, you should have a heck of a time pressing it back in.
When you do decide that it's time to pull that bad boy out, pop out that piston and inspect it, as well as the piston bore. BTW, for safety's sake, place a piece of wood where the brake pads live before you put shop air to the bleeder hole to remove the piston. Do this very slowly, you would be surprised at how fast the piston will want to eject from its home. It scared the crap out of me the very first time I did this.