the sport package for the X just adds appearance items, like unique spoliers, badging, paddle shifters, different front seats, and bigger rims. Should give you quicker steering and upgraded brakes for the 2011+ X models also. But the engine and transmission is the same Sport or non-Sport. So i highly doubt something is incompatable with the AWD system. The AWD system is routed through the VDC system based on the diagrams ive seen, but like the ABS, the AWD works independent of the VDC when "VDC is OFF".
I had a simular thought as you, wondering if the VDC counter acted the AWD system by cutting power instead of trying to shift power first with the AWD system. I think i even have a post where i asked this question on these forums... found it...
vdc-on-a-g35x-is-it-with-or-against-the ... ?hilit=VDC Here is a quote from the post:
"Ohhhhh ok the awd is an input to the vdc system! now it makes sense... VDC is Top Dog as everything comes through it. That means when its off each system is independant and doesnt have its Captain VDC..."
so my guess, is the VDC is kicking in extra hard for some reason. If you are getting a AWD light, the transfer case has over heated, which points to why you have to let the car cool for 30 mins. Ive owned two X model Gs, experimented a lot lol and have never gotten the car to overheat the transfer case, which i suspect is going on.