Interesting theory. I would like an experiment of very accurate measurements of the Earth's gravitational field at different points in its solar orbit. Unfortunately, the hypothosis behind the experiment dictates that those measurements cannot be made on Earth or near Earth, making execution just a bit of a challenge.
I bet you would find variations on the order of 10E-13 at different orbital positions.
Interesting idea. We once tried after many drinks to try to hit the Apollo mirrors with a laser (yes more powerful than a pointer). The results of the test are in dispute since we passed out before verification. Damn tequila. I still think we hit it and got a return.