Yes, that kind of thought process is the right sort of way of thinking about gravity
If I feel like it tomorrow I will program something in flash where something orbits something, and you can press a button to suddenly double gravity and see what happens
To expand a little bit on what I was saying, there are other things to consider like the eccentricity of orbit and the exact point of orbit the planet is at when the gravity suddenly changes, but these are all consequences of elliptic orbits. The stuff I was saying is a special case of a perfectly circular orbit. But in general yeah, the same sort of thing will usually happen outside of extreme cases, like really oval-shaped orbits where the speed changes dramatically between the minima and maxima of the orbit's position relative to the sun.
Another way of thinking about it is that since Mercury is closer to the sun than us, it feels more gravity from the sun. Because of this it orbits closer, and faster, than we do.
If String Theory is somehow ruled out, I think at least one of it's supporters should be kicked in the balls, yeah. It's only fair to be honest.
EDIT : I wrote a program where you have an object in orbit of another. The blue circle is like the Sun, the green circle is like the Earth. To make things interesting, the orbit is slightly elliptic. The Green line is where "Earth" moved before gravity doubled, the red line is the path "Earth" took after gravity was doubled
If you press the button to double gravity in a different place then you can get different orbits. Feel free to experiment with it here:http://dl.dropbox.com/u/6934906/Gravitation.swf
I was lazy and didn't make any functionality to restart the program so you'll have to reload it every time you want to try a different thing