On the older models such as mine, 2002, been using Mobil 1 10w30 for 15 years. Many of us GM guys are using motor oil. Mike L of Lynwood transmissions strongly suggests synthetic motor oil due to evaporation.
I don't know if they updated and fixed the pump rub problem the older models have, you might check and see if they sell a kit "plate" to alleviate wear thru of the transfer case housing.
eta; its been fixed 2008. Does not apply to your T case.
08 Tribeca 82k PUP 5w30 wix
06 Accord Hybrid 131k PUP 5w20 wix
02 Chevy k3500 97k Delvac 1 esp 5w40 wix
00 F350 133k Delvac 1300 15w40 wix