That's interesting. If your math for the springs is good, you might need to play with the damping settings instead, because at higher suspension values you get a narrower range of working damping values. I think my spring strength is internally set to 1500 and the damping value is 100. Any much more or less than 100 damping makes the suspension unable to sit still.
Also yes, I did the exact same thing - a sideways capsule under the front bumper with 0 bounce/friction, but it didn't solve my issues because the car was going fast enough that it'd clip into the track between timesteps and get spat out.