Dear Jacek,
As I told you in my Essay page, I have read your peculiar Essay. Here are my comments:
1) I do not think that your statement that gravity is transmitted instantaneously is correct. In general relativity the speed of gravitational interaction is finite, presumably equal to the speed of light. One can indeed show that the problems that you suppose to exist, i.e. unstable planetary and stellar orbits (aberration of gravity), are not suffered by a static field in general relativity.
2) I did not know the Thurston geometries. Thanks for pointing out it to me in your Essay.
3) In your table in page 3 you claim that the spin of gravity is not applicable. Why? Although we do not have a full theory of quantum gravity in the weak field approximation gravitons have spin 2.
4) One of the greatest problems obstructing the geometrization of the electromagnetic interaction is that there is no electromagnetic counterpart of the equivalence principle which is the foundation of metric theories of gravity. This is because, while the ratio between gravitational and inertial mass is universal, the same does not apply to the ratio between electrical charge and inertial mass. How do you think to circumnavigate this problem?
5) Concerning your proposing the evolution of information concept, how holographic principle does enter in your geometric picture? Is there room for it?
In any case, I found your Essay interesting.Thus, I will give you a high score.
I wish you best luck in the Contest.
Cheers, Ch.