However, my question just now shifts to what causes the "freefall". I imagine that if you take a ball and funnel into space, and push the ball around the edge, that without some other force, (like blowing on it), the ball would just spin out of the funnel all together.
I will try one small bit that wasn't put so clearly that might clarify it, and then respect the "take it to another thread" request...
Consider space away from anything large. It is open and flat, right? Say you have an object. It got a push some time ago, and is now just cruising along. If nothing else pushes on it, it'll keep cruising along in a straight line, right?
Well, now put that object cruising along through a curved spacetime. Imagine, what does a "straight" line look like in a "curved" space?
Think about driving in your car, in a straight line down the road. Now, zoom out in your head. Way out, until you see the curve of the Earth - and you realize that "straight" line you were driving in is, from teh point of view of someone not on the globe, curved!
This is what is happening in your example - you keep thinking that the spacetime is flat, and straight lines are straight - but near a massive body, the spacetime is curved, and the "straight" lines near it - the lines that are parallel and wont' intersect - are *curved* from the point of view of a distant observer.