Barry, if your rim if finished baking before your cheese is bubbling and tan, there's a few things you can do about it.
1. Decrease your thickness factor. The thicker the dough, the more water you have in the undercrust, the longer it takes to boil/turn to steam, the less heat is transferred upward to the sauce and then cheese. Bottom heat plays a huge role in proper cheese melting/bubbling/tanning.
2. Use less sauce.
3. Use less cheese.
4. Use room temp or slightly warm (not cooked) sauce.
5. Allow your cheese to come to room temp before using.
6. Make sure you're going with a traditional coarseness of grate for the cheese and not cubing it/breaking it into chunks.
7. Temper your dough a little less so the dough is cooler when you stretch it (remove it from the fridge closer to the bake).
Out of all the options, decreasing the thickness factor is usually the most effective. Bear in mind, as I said before, this is NY style I'm referring to- also, being NY style, I'm talking about low moisture (aged) whole milk brick mozzarella (such as Sorrento or Polly-o)- the supermarket stuff.