My suggestion, both for avoiding mosquitoes and getting your layover day in there somewhere, is to bite the bullet and push for a long day the first day. Aim for Jack Creek, and yes, that can be a lot of rowing, but that's how we always have done it (even with camp kids and outward bound youth paddle boats) and once you cover over 20 (maybe over 25) miles the first day, it really frees up the map for the rest of the trip. Also- after Jack Creek the water really picks up speed and the bugs are way, way better.
A lot of people are tempted by the campgrounds on or around Stampede Flats: the bugs are still man-eaters at this point. I've never gone as late as september, but the bugs are going to be kind of epic this year, so I would just consider them a major factor, and if they turn out not to be there, awesome- you'll be able to tell at the put-in.
So that would be my advice- sacrifice 'relaxed' for just the first day (everyone's still energized then anyway, right?) and set yourself up to have options later on.