If the bias isn't fully open it can trap air in it, and you wont get a good strong flow of fluid thru to the rear brakes.
Yeah just unbolt the caliper and hang it upside down to bleed, then refit.
Problem is, if the pedal goes to the floor you normally end up tearing the seals inside unless its very new. After this the cylinder is never the same again

This doesn't explain the problem with the rear caliper though, that is most probably air in the system
