Since the door jamb's 37 psi is for the default 3.6L engine configuration, and the diesel engine is much heavier, should cold pressure on EcoDiesel Wranglers be 2-3 psi higher to match the 37 psi for 3.lL engines?
You are over thinking this. Tire pressure should be somewhere between what manufacture states and what gives you the best pattern during a chalk test. If you like driving a squirrelly log wagon by all means air to 40 psi.
I have stock a JLUR diesel with the OEM Falken off road tires. The correct tire pressure for me is 37 psi. I do air down for some trails, but I set tire "cold" pressure at 37 psi for highway driving. As the tire temperature increases, so does the air pressure.