The reservoir was full to the brim. There were no air bubbles coming out of the rear ones. New brake fluid was flushing out at the rear without any issues.

New fluid coming out the rear can still be air entering at the reservoir as you bleed...That was my point.
You have to make sure the fluid level stays high in the res as you open the bleeders..and then recheck the level before going to the next bleeder.

The other possible is you have an internally leaking MS [ fluid bypassing the piston cups under pressure.] You can usually tell that by holding the pedal down hard for a min. and watch for sinking pedal..........

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A Dalton