Just my opinion, but I think that very small window in early Sept is one of the few true lower (note, not low) crowd times around. We've done several smaller trips around a
MNSSHP during that time the last few years. If we didn't have school schedules to deal with, I'd absolutely do a long trip like yours probably every year.
Pros - More manageable crowds, among the lowest resort rates of the year, resort discounts are sometimes easier to find, good time to catch a MNSSHP and F&W (F&W used to start later in Sept but since last year has started end of Aug)
Cons - Hot as blazes, free dining does a good job at filling rooms and gobbling up ADR times, some earlier park closing times (more like Jan/Feb, although this varies by the day)
I think it's important to not let the "low crowd" expectations get too carried away in your head - it's always some shade of crowded. It can just be more manageable overall.
Happy planning!