Adding to the good info Bill provided (especially about the trail assn and guide book) ...
You were asking about early Sept ... there are few historical climate data sets for North Shore locations but I did find about 115 years of climate data from Two Harbors.
For the first half of September:
the coldest 10% of days were 27F-42F
the mean low temp was 50F
the warmest 10% of days were 79F-92F
the mean high temp was 69F
60% of the days had zero precip
15% had precip >0 but <=0.1 inch
13% had precip >0.1 but <0.5 inch
6% had >0.5 but <1.0 inch
6% had precip >10 inch
That said it is entirely possible (but not likely) that it'll be cold and wet your entire trek, he-he
Your idea of parking the car at mid trek for re-supply should work if you use the shuttle service as you propose ... be aware that the shuttle runs only on Fri, Sat, Sun and major holidays. Alternatively, you can arrange to meet the shuttle at a scheduled trailhead stop for a food resupply if mid trek is on a day the shuttle runs.
How busy will it be? Backpacking usage has grown steadily the past 10 years. If you go on the nicest stretches on a holiday weekend you should expect to share campsites with others at least some of the nights. You'll also see quite a few day hikers, especially in the state parks, even more so in Tettegouche (east of Silver Bay).
Bill's suggestion of Oberg->Cascade River is a good one. You mentioned Beaver Bay or Silver Bay and eastward ... very very scenic but very very rugged.
Have a good trip!
You asked about parking, most trailheads allow overnight parking, the highway waysides have signs saying "NO". If parking at a state park you'll need to purchase an entry pass and also ask where they prefer you to park long term ... they'll normally ask for vehicle info so they know you're expected to be gone overnight(s)
regarding insects, the later the better. I have pretty high mosquito tolerance but would still want a bug bivy under a tarp or a shelter with built in screening ... unless it were after the first hard frost.