A 911 should be solid enough that if you hit a bump you will feel it but it shouldn't have a jarring rattle to it. You might check the wheel bearings. If they are even slightly loose it could rattle your teeth.
If that isn't it then I would look for a set of 15" 6 & 7s. A wider rim for a given tire size will stiffen the sidewall. If you use a narrower rim it increases the curve of the sidewall and adds compliance.
God, it bothers me to give advice to increase compliance...
AAAARRrrrrrgggghhhhh....
I can't take it!
Go buy a kidney belt and replace the stock bars with 22s and 29s and become one with the road. (I wonder if you can get potholes in your teeth?)