Proportioning valve / rear brake problems

Is there a chance that the P-valve is plumbed backwards?

You may have 2 issues.
It seems like the front brakes are not working,or not working right; and there is definitely a problem in the rear.As to the rears, only one side is working, the side that is locking up.
If it was me I would isolate the systems and work on one end at a time.

Yes the R-valve ought to be closer to the M/C than the P-valve. However, I don't think it's a big deal. It's job is just to keep a little pressure in the rear wheel cylinders to keep the rubber cups tight against the cylinder walls.This tends to keep leakage to a minimum, back there.