Are you so sure that you wouldn't be harmed in an extraordinarily strong gravitational "field", with field lines parallel to your body?
I imagine that the difference in force exerted on your feet vs. your head is significant, in raw Newton's rather than as a percentage. The r^2 is basically constant across the length of your body, compared to M, but it's not actually constant, and when M is so large, I imagine even small changes in r^2 lead to (relative to our scale) large changes in F. Is my intuition wrong?
You are saying the same exact thing as the comment you replied to. Differences in the force at the feet and head is exactly the gradient of the field. If you have no gradient the forces are equal everywhere.
I imagine that the difference in force exerted on your feet vs. your head is significant, in raw Newton's rather than as a percentage. The r^2 is basically constant across the length of your body, compared to M, but it's not actually constant, and when M is so large, I imagine even small changes in r^2 lead to (relative to our scale) large changes in F. Is my intuition wrong?