I have installed the game to my Xbox 360 hard drive, yet the loading times between races are still very slow. Is there anything else I can do to speed the loading times up?
No. About the only way you would be able to speed things up would be to figure out how to hack your 360 to put in an SSD in place of the hard drive. Given the way the firmware on the hard drives is secure, that's currently impossible. Sorry for the bad news.