I want to add that oversteery cars are a lot easier to handle on a pad than a wheel. For this week's daily race A (karts at Brands Indy) I had a lot of trouble on the wheel and way off pace. Then I read someone recommending it's easier on a pad, and within a few laps of adjusting (I haven't raced on a pad since GT5P way back in 2008), I was already beating my wheel time and got much closer to my usual gap to the top times. There's this "invisible hand" that keeps the rear end more in check and of course it's easier to countersteer quickly when it does step out.
So yeah, if you have trouble with the Stratos (or any other oversteery car), might be worth taking out the good ol' Dualshock