I think that is the "transfer case roll stop." All of mine were like that with the big center hole. I know they make new ones with extra rubber in them. Check your actual Tcase/transmission mount, mounted on top of that cross member. Mine was completely severed after 15 years. There is a small metal strip bolted through it too for when they fail. Check your motor mounts too.

I just want to tell you both good luck, and we're all counting on you.