Instead of shipping the transfer case back to Advance Adapters, I decided to replace the input shaft myself. Replacing the input shaft myself saved time from not having to wait on shipping both ways and gave me the opportunity to write a "how-to" which will hopefully help someone out in the future.
Advance Adapters sent the 31 spline input ring assembly with the bearing and seal installed already. This eliminated the need to press out the input bearing and replacing it along with the input seal. Before the 31 spline input goes in, we obviously need to take out the 23 spline input.
The first thing I need to do was get the Atlas on a work bench and flip it upside down without damaging the breather. You can either remove it or put the Atlas on a block so it doesn't sit on the breather. You will see the the inspection cover being held on by 14 bolts. Remove these and remove the inspection cover by utilizing the pry points on each end.
Once the inspection cover is removed, you will need to remove both the front and rear cluster pin bolts then push the cluster pin out from the front while holding the cluster gear with one hand. Lift the cluster gear from the case being careful to not let the needle bearings fall out from inside the cluster gear. Once the cluster gear is set aside, remove the two thrust washers.
Once the thrust washers are set aside, remove the 6 bolts holding the input ring to the Atlas housing and remove the input ring assembly. Remove the drive gear from the input assembly by first removing the snap ring then the drive gear. Advance Adapters says this is a light press fit, but sometimes it can be pulled off by hand. Install the drive gear onto the 31 spline input assembly and make sure the snap ring is seated in correctly.