Chip,
I had a lot of trouble with the rusted old bleeder valves in my jag calipers. And, I had a terrible time getting the air out of my system. The solution that worked for me was to remove the right front bleeder nipple (can I use that word here
, wrap it with plumber's teflon pipe thread tape, screw it back in almost to the bottom, fill a large medical syringe with brake fluid, connect it to the prepared brake nipple and push the fluid in while watching the brake fluid reservoir. When all the air bubbles stop coming up, I bleed the rest of the wheels the normal way.
It worked for me,
Paul