Does the in-car view share the same steering sensitivity as the chase cam? Inside the car the pillars and dash swing across the screen, so the same input tends to feel twitchier, and a lot of driving prototypes end up with a slightly softer steering curve for the cockpit camera only. Might be worth swapping views mid-corner in a playtest to see if it feels like the same car.

Cockpit view is a big jump for feel. One small thing that usually helps a lot: a touch of camera lag or head-bob tied to acceleration and braking, so the view isn't rigidly locked to the car. Are you planning to let FOV widen a bit with speed too?