Your so-called 'nonexistence of dynmaic solution of 1915 equaiton' comes from a trivial error of your misunderstanding of 'dynamic'.

In four-dimensional space-time, there is no 'dynamics'. Gravitational wave surely propagates in three-dimensional space.

It's utterly unclear how your 'anti-gravity' coupling would turn the thing upside down.

Of cause, your real problem is that you lack mathematical proficiency to deal with this type of problems. If you sincerely want to test your whimsical 'idea', you shoud, I suggest, find a good mathematician or a good theoretical physicist to collaborate with. Hand waving does not solve real problems.