Sounds good to me. I think this moose season marked my fiftieth.
I live further north so the best two weeks here are slightly earlier... probably September 20 to October 5 (which is still darn close to what has already been stated).
This year we killed one bull in the last week of September and the other in the first week of October... but then of course, that is when we are hunting.
If you have a lot of competition, it might be worthwhile to head in a few days earlier, but if it's warm, your plan might backfire.