Just to update the situation, I told Codemasters what I thought about my save file being corrupt and they've never heard of that being a problem. But they want me to get to the point in my new career mode where I can race the DTM's and V8's, since I told them that's mostly what I race.
After thinking about it, the cars early on in the game really do feel loose and kinda hard to control, so I probably wouldn't feel the pull as much as I do with the tighter cars later on in the game.
I'm starting to think Codemasters has never heard of this before and they don't know what can be done. To their credit, they've tried to help, they just don't seem to have the answer.
I may or may not keep going with that new career mode. Since the problem is pretty much just a minor annoyance so far, I may just accept it and move on. I still have good control, it's just that I know it shouldn't be pulling left like that.