Hmmm, i was using a Griving Force GT on SR3 for a while, no problems here. You have the logitech software installed? when you bring it up, is the wheel properly centered when at rest? I would also make sure the wheel is set to 270 degrees for testing as that's probably easiest. And then try changing the force spring setting and see if that makes a difference.
I've seen something vaguely similar happen in some games when you turn the wheel gently one way, and it kinda kicks back and forth across centre gently. Is that the issue? If it's big enough to be a problem, or too sensitive for you to hold the wheel on center to stop that effect, maybe you could try adjusting the deadzone somewhere. In TP it's called Stooz zone, and you should try setting it in the logitech profiler and also the FFB plugin ini (if possible). Maybe some combination of factors would help.