If the room temperature is better with the doors open the return is not optimum.
Some of your other observations hint at less than desired Supply Air.
Can your manometer measure 0.01".?
IF Not, you may not really know whether the areas are actually close to the same pressure.
Velocity pressure = 0.01" is created by 400 F.P.M. = (400/4005)^2
It's sounding like the Supply Air delivery is a problem.