Rear brakes lock up... front disc

Dang, with all those problems you should just drive down the hill and give the car to me! :D j/k

My Challenger did the exact same thing with its 10.8" front disks and 10" rear drums. I went to 11 3/4" disks in the front and 11" rear brakes with no other changes, balanced perfectly now, although I don't recall which wheel cylinders I have on the 11" drums.

You mention that everything is new, have the pads and shoes been on the car long enough to be broken in? Were they installed at the same time?

Otherwise, at this point I would install an adjustable proportioning valve. Not sure why it didn't work for your other car, they should be more than able to balance the braking front to rear when adjusted properly.