Is the 6.2 gonna have enough umph to push the truck with 37" tires and 3.73 gears? That will put your new effective ratio at 3.13:1. If you leave the 4.56's in with the 37" tires, the new effective ratio is just over the 3.73:1 target. (3.82:1)
Found this on a Superlift gearing/ tire size website:
The chart is divided into three categories. The rpm highlighted in black are optimum for the tire size and ratio combination. These will most closely give you the best overall drivability. If you're looking for a ratio that will give better fuel economy for highway driving at the expense of some acceleration and overall performance, choose a ratio in the yellow shaded area. If you're looking for a ratio that will improve acceleration and towing power at the expense of some fuel economy, choose a ratio in the blue shaded area.