"The answer to the CHina Syndrome question is that you would come out with your head pointing up, even if you entered the hole with your head pointing down"

Amos, think a little more; you're right, of course, in that when you come out of the hole on the other side, you are going "up", away from the earth's center of gravity. But that doesn't mean you would come out head up , unless you entered the hole with your head pointing down; not "even if" you entered head down. Passing through the center wouldn't necessarily imply that you would flip end-for-end on the way. I think I gotcha!