The tire pressure on the door is not anything other than a recommendation. It is a good place to start with a new set of tires, but the brand, type of tire, style of driving and the weather conditions will determine the correct pressure for the situation. With a smaller sidewall one would think that you could use less pressure compared to a similar tire because the stiffness of the sidewall should increase. I have a set of recently purchased Falken tires on the rear of my SRT6. They are very squirrely at 32 psi and must be run at 40 psi to keep the rear stable for spirited driving.
If your steering feels "vague" then you may need to change the steering stabilizer. Easy job most of us do ourselves and not expensive.