It is impossible to get matching gear ratios when you have different sized ring gears... unless you happen to get a ring gear that just so happens to be a multiple of the other ring gear.
Ratios are a measurement of the diameter of the ring gear to the diameter of the pinion gear. The easy way to compare sizes is to go by tooth count.
As mentioned before, it is often impossible to end up with matching gears if the ring gears are different sizes.
Since the dawn of time, vehicles have often had different gear ratios front and rear. As long as they're within 1% it doesn't matter. In fact, your favorite competitor (Ford) ran certain vehicles with a 1.6% difference. You shouldn't be running in 4wd on something that isn't slippery and can let the bind come out of the system anyway. AWD (such as the unlocked position of the NP203 or any other differentialed transfer case) it doesn't matter.
Maybe none of us should run lockers either... after all, if the tires happen to be a wee bit different in diameter we might done blowed up our axles.
Think about this for a minute. All of you people (and I'm willing to bet you yourself) that run the same air pressure in all four tires are actually subjecting your transfer case to more than 1% difference. The rolling circumference of the tires are quite a bit different. That's why smart people run varying air pressures front to rear. Well, that including a whole slew of things like tire wear, performance, and ride quality. Usually a 2-3psi difference.
Anyway, back to the original question. You need a different (4 series) carrier for 3.73, 4.10, 4.56... et cetera than for a 2.76, 3.08, 3.42 (3 series). The ring gear is 8.875". If you don't believe me, measure it.
You should buy a ring and pinion of decent quality (Yukon... $160. Richmond... $200) and buy a master install kit. You'll only need to buy one master install kit for that axle because chances are the next time you do the same axle type you'll have all the shims you need.