I've read the Fomalont and Kopeikin's experiment, and though very interesting and supposedly proves the speed of gravity, I feel there may be a very "simple" experiment that will make a comparison of the speeds, with an event that occurs every day, and may be tried by many groups with the measurement capabilities that are currently available on the ground.
This is the experiment I'm proposing:
Use gravity sensors of the highest sensitivity to determine the "peak" of solar gravitational pull in the vertical direction, and compare this peak time with the peak of solar radiance that occurs at noon.
If the peaks are coincidental, then the speeds are the same. If there is a lag of eight minutes of the peak of solar radiance, then gravity is not light speed limited.
We know the sun's actual position is eight minutes shifted from the observed position, but I have not seen any experiments that try to demonstrate this.