I read that the much denser LOX is on the top[*] of the ET, with the
LH below it. This seems counter-intuitive. I would think from a
structural point of view, you would want the heavier stuff on the
bottom, and it would also move the vehicle's CG aft, which I would
think would improve aerodynamic stability.

I assume NASA didn't just flip a coin to decide which goes on top, so
there must be more to it that that. What's the real answer?
[*] I'm not sure what the coordinate system is here. Is the pointy
end the top or the front?