I'm not sure that this captures the physics accurately from the perspective that you're describing here. The extreme time dilation that occurs as you approach a

I'm not sure that this captures the physics accurately from the perspective that you're describing here. The extreme time dilation that occurs as you approach a black hole's event horizon is really a "global" effect rather than a "local" one: it is defined by the relative difference in how time progresses close to the black hole vs. very far away. When you're falling through the horizon (particularly for a black hole so large that the tidal forces at the horizon aren't deadly), your whole body is "close", so there isn't substantial time dilation between your head and your feet. This is a little bit weird, I know!