I should really clarify my previous post. When I said the a doubted a car could turn fast enough to harm a pizza I meant purely rotationaly. Imagine a pizza rotated about the middle so that it spins around. Now imagine how fast one would need to spin this pizza or how hard one would have to accelerate its rotation to do it any harm. I would imagine that it would need to be quite fast, and while his driving is amazing the maximum rotation rate is likely not in excess of 180 degrees a second. Not near enough by itself to harm a pizza.
The issue is the sideways g-force that is generated in the turn. This defiantly would harm a lowly pizza, but this sideways force is something the accelerometers can sense and your platform can realign to be straight down relative to the pizza. As far as the pizza is concerned gravity just got a bit stronger, but any sideways force is countered by the force of gravity which is no longer straight down on the pizza.
A well weighted suspended platform could work well and would be simpler, but without damping you could get oscillations at its resonant point that could harm the pizza too. After any sudden stop you would get a swing-set effect. Damping would help, but it would also slow the response to a sudden impulse. Good gimbals with a pair of positional servos could likely react faster than a simple pendulum without any noticeable oscillation. I would bet your main sensing loop could run at least a few hundred times a second making the system very low latency. The limit would be the maximum rotation rate of your servos, but they can be quick as well. Without the motor the platform is essentially a proportional controller. If you do a little looking into controls theory you will find why a proportional, integral, derivative controller (PID) would result in faster rise times with much less oscillation.