The C-17 would be the best choice of all. It's proving itself to be the Rolls Royce of airlifters, and well-liked.
BUT...
We're already using up airframe time on them faster than new ones can be built. If I was "thinking outside the box", I'd use Army funding to second-source the C-17 to another airframer, and then give them to the AF, with the orders that that number of aircraft will always be instantly available to the Army on a moment's notice. Heck, I'd even have the Army pay for the slots for the AF guys that flew them.
I think the Army would get far more benefit, and have far fewer problems, buying $10 billion of C-17 over $10 billion of Stryker. Far fewer miracles are required that way.