I'm not too worried about the weight sloshing around. It's only twenty pounds, and if needed we can just put the pivot point at center mass of the pizzas which would make any movement unnoticeable to the rider.
You are correct that motorcycles lean to overcome centrifugal force, but a motorcylist can also lean his/her body for the same effect. The ideal angle for the pizza/the angle for center mass, would then be somewhere between the bike and the rider. Sometimes the bike is leaned more than the rider. Sometimes the rider is leaned more than the bike. The pizza on the back is sloshing around the whole time.
Also think of it this way: You have two pizzas. Pizza one is riding along in the passenger seat of a car. Pizza two is on the back of a bike. Both vehicles go through a turn at the same speed. The pizza in the car made it. What would you expect to see inside the pizza box strapped to the bike that was leaning through the turn?
Second scenario, same situation, except that the pizza on the back of the bike remains at the same angle as the pizza in the car. Pizza in the car survives. What about the pizza on the bike?
Here's two home made gyro cams operating on the same principle. THe first one is just made with a servo that has a gyro in it, designed for RC airplanes and quadcopters. In the air im sure a quadcopter isnt pulling any G's, but on the bike you can see that the camera moves freely from the bike, yet the horizon leans a little with whichever way the bike is turning, I'm guessing at the angle for center of gravity. The second one does a surprisingly good job of staying perfectly horizontal. I wouldn't be surprised if some of that was fixed in post.
http://blog.capinc.com/2011/11/the-motorcycle-gyrocam-project/