Hi Brendan, you can reduce the rust by going to Home Depot and buying "Concrete and Metal Prep", sometimes it goes by other names, it's a green solution. It's a metal prep, similiar to used on bare metal on cars. Cut it 50/50 with water, put in a spray bottle, and hit sign in 5-10 minute intervals and wash it off. Don't try to remove all the rust, you dont want to go down to bare clean metal, you are just cutting the rust down some. Works best on formerly white areas in my experience.
You have two problems tho, there is a red spot that I might try to remove, and that area around the pepsi has bigger rust spots that are kind of problematic. So anyway, the approach above has some risk, but so far I've used it to reduce "too much" rust pretty successfully, it's just not a miracle cure and you dont want to do too much.