I had an introductory astronomy course, so all in all I'm not too familiar with stellar models beyond the basics... But there are many technical as well as practical difficulties I would think when you would try to determine the mass of the sun accurately enough to estimate G (even if you ignore that the model itself depends on G). One I can think of is the fact that stars lose mass throughout their lives, so we would need to know the age of the sun in the same order of precision, which is impossible.
But probably there are models for the trajectories of the planets, given a star with a slightly decreasing mass but I doubt that they would be accurate enough for comparison with our present situation.