arthur, I regularly make 2 minute pizzas with my cleaning cycle and 8 minute pizzas at 550. Like you I have found that I absolutely have to use different cheese for each type of oven. Regular dry mozzarella just needs to melt for a while and it doesn't taste good with a 2 minute melt. If you have access to grande fresh mozzarella, or a god quality buffalo mozzarella imported from Italy they are my favorites for my 2 minute pies. The buffalo mozzarella may seem sour at first, but once it is melted on your pie and properly seasoned it can produce the best flavors I have ever experienced with pizza cheese. The key to using this wet packed cheese is how you prepare it. First I slice it or chunk it. I then lay it out side by side on a stack of at least 5 paper towels. I top it with another 5 paper towels and flip over after a 10 minutes or so. Then I replace the paper towels on top, flip, then replace the other stack of towels. Depending on how fresh the cheese is you may need to do more than one changing of the towels. The fresher the cheese, the less moisture it will weep. If your cheese is past it's prime it will just sort of smoosh and will not slice even with a sharp knife. When the cheese is fairly dry I take the top layer of towels off and salt the cheese. I have found that I prefer this to salting the whole pie. With this type of cheese a good splash of olive oil is possible because this fresh cheese does not seem to be as greasy. The combination of a good salted fresh cheese and oil is the most addictive pizza topping I have ever found. I used to be a pepperoni guy, but now I am very happy with plain pizza.
Now, if this is too complicated, or you are having a hard time finding fresh cheese there are other options, but I have not found them to taste quite as good. The next best option is to mail order cheese from this company http://www.allevadairy.com/
. This might bring back some really great memories of growing up in NY. Finally, the cryopack semi fresh cheeses seem to be gaining in popularity at the moment at normal grocery stores. This cheese is called "fresh", but is not packed in water. Instead it has a form fitting plastic coating. It contains a little more salt than fresh mozzarella, but definitely can still benefit from some oil.
Try calling around to Italian specialty shops in your area to find out if they import buffalo mozzarella. If they do, ask them if they will notify you when they get in the fresh stuff. I have found that once it sits in the store for a week it is not worth buying. The grande or poly-o fresh mozzarella seems to last much longer.