I went from the 3.73's to 4.88's w/ 34" TBs. Its not a bad combo, but its still a 4cyl. My auto isn't in its best shape, but rpm near 70mph is ~3350-3400. A tad higher on the tall side, but acceptable. Since you are going to the 9", is there a plan to upgrade the front so deeper gears can be brought into the picture. If you plan to hit a tire size in the 37's, I would atleast minimum hit gears in the 5.30's.
Do note, 5.89 is available in the 9" and 5.86 in the low pinion D44. That would make an awesome combo for the 37" tire. Next, with a tire size that large, is the Jeep still to be a daily?