You're not the first person who has had this issue. At this point I'm struggling to find a resolution. I use the same wheel and I've never once experienced this problem.
I usually tell people to check if the "virtual gearstick" option is enabled. It causes your mouse to behave as an H-Pattern shifter, and it can be super sensitive to the point where, the slightest movement of your desk (from force feedback or whatever) causes the car to shift.
I'd suggest try turning on the virtual gearstick, restart the game, then turn it back off?
Otherwise I have no idea. Best of luck brotha. I'll keep digging.
Also, are you using the paddles to shift or the H-Shifter?