if you can rotate the axels(spin one of them with your fingers) without activating the diff, then your drivetrain is probably not causing this sudden stop. I did notice the center pulley binding when you screw the center plate down, but no where near halting the entire drive train.
This "sudden" stop, is it like you applied the brakes? what happens when you do apply the brakes? does it stop faster? have you tried resetting the setting on your radio? I helped a guy that had a similar problem, and it finally went away when we did a master reset on his radio. Also make sure you properly set the esc after that.