Updating:
Biggest thing was having 3 people. My brother and I used large screwdrivers on both sides to hold the plate in place, while my dad pushed / tightened the bolts holding the transfer case to the transmission. I fully acknowledge others may have had an easier time, but this helped us make things happen correctly.
It also should be noted that putting the gearbox in 4th while installing the transfer case is crucial. We had the shift fork get stuck a couple times and had to re-do things.