Tech Week! One Man Half Brain Brake Bleeder.

The pump is capable of 75 psi so it should have no problem pushing past any residual valves.

 

If the piston is still depressed when pedal is all way up, you can't pump fluid in reverse as the port from cylinder into reservoir is covered. Check to see if you have a little free play on master cylinder push rod and that master cyl. piston is pushed all the way back by the return spring.
Dave