You're truly asking good questions.
The answers essentially come down to what do you hope this hunt to be? What does "decent hunting" mean to you? As hunters we can differ in what we seek out of our hunts, and that's ok. Regardless of dates, you will see moose...perhaps far away...but what are you hoping to experience in this hunt?
Moose rut is a progression...specific calls and calling tactics vary through the progression. Learn all you can about the rut progression, e.g., bull/cow behavior from early to late Sept. As you learn more about the rut progression, then ask yourself what would be a "descent hunting" experience for you in that progression.
As just one example...I prefer calling bulls as close to me as I can for several practical reasons and the thrill!! Given my preferences, early Sept is not my personal choice...sometimes doable, but not ideal for what I seek.
The very best to you on your Alaskan adventure...moose hunting in remote Alaska is a different world...a lot of work when you get one down...and the meat is excellent! I look forward to that hunting experience every year!