Dear Sergei,
I have been studying the references that you gave me in my FQXi forum and I find they fascinating. I am still studying LITG, but it seems to be some kind of gravitomagnetic approximation to the field theory of Gravity (FTG).
LITG uses scalar and vector potentials, whereas FTG includes a tensor potential as well because the source of the gravitational field in FTG is the generalized stress-energy tensor \Theta^{\mu\nu} instead of a four-current as in LITG. Similar remarks about the expression for the gravitational force in each approach.
The reference on Strong gravitation does not give the Lagrangian. Is the LITG Lagrangian used in Strong gravity after substituting the gravitational constant by \Gamma?
Let me add that the "4/3 problem" is solved for electromagnetism in
Action-at-a-distance as a full-value solution of Maxwell equations: The basis and application of the separated-potentials method 1996: Phys. Rev. E 53(5), 5373-5381.
Chubykalo, Andrew E.; Smirnov-Rueda, Roman. Erratum: Action-at-a-distance as a full-value solution of Maxwell equations: The basis and application of the separated-potentials method [Phys. Rev. E 53, 5373 (1996)] 1997: Phys. Rev. E 55(3), 3793--3793. Chubykalo, Andrew E.; Smirnov-Rueda, Roman.
Reply to "Comment on 'Action-at-a-distance as a full-value solution of Maxwell equations: The basis and application of the separated-potentials method'" 1998: Phys. Rev. E 57(3), 3683--3686. Chubykalo, Andrew E.; Smirnov-Rueda, Roman.
Using the same mathematical and physical analysis the 3/4 problem is also solved in gravitation --see also ref [11] of my essay--
Regards.