Thanks LiamBeran!
@bmarci I reverted back to what I used before but I took the s and a variables idea (slipratio/optslipratio) and use this to create a friction ellipse instead of a circle.
Also, your last paragraph about not reducing the forces equally gave me some ideas. I'm now trying to reduce the lateral force with longitudinal force ratio (s variable) in an inverse x^3 graph. So the lateral force is not affected much until the longitudinal force start reaching it's peak. Then the lateral force drops quickly. It show some promise. Now I get better grip when turning, but still being able to do some (half) donuts.
lateralForce *= 1f - Mathf.Pow(Mathf.Clamp01(ratioLongForce), 3f);
Currently I'm getting snap oversteer so I can't drift in corners. Maybe it will help to do some lerping when going from static to dynamic friction coefs.