I’d think 8 to 12 miles per day would be reasonable. The lakes you’ll be on are big enough that wind can be an issue, which can mean paddling early in the day when winds are typically less, and laying up in camp if paddling is difficult or unsafe. I used Ecopelagicon in Rangeley for a shuttle last year. You could also call L.L. Cote’s in Errol (big north country outdoor store) and see who they recommend for a shuttle driver. If you can pick someone up in Errol on your way to the put-in that might be the cheapest shuttle option. Bugs are typically gone or nearly gone by late September. Nights will be chilly, and you could easily see frosts but snow is unlikely. That’s getting into foliage season, and it is a really nice time for a paddle trip, although the days are shorter and cooler.
You or your friends should buy a copy of the NFCT section map, which covers the 40 or so miles from Rangeley to Errol. Campsites through there are mostly by reservation, but off season when you are going there will not be many other people camping on the lakes. Maybe that late in the season reservations are optional, I don’t know.
If you go all the way to Errol there is a lengthy portage along the Rapid River from Pond in the River/ Lower Richardson Lake down to Umbagog Lake. The portage is several miles along a jeep road. The Rapid River is expert level whitewater, so paddling it is not really an option! Portage wheels for the boats would be helpful, I bet.
If you are not set on ending up in Errol then another option is to do your trip (in either direction) between the town of Rangeley and South Arm Campground on Lower Richardson Lake. There’s a recent trip report on the NFCT website for that trip. With 4 nights on the water you’d have extra time to fish, cook, explore from camp with unloaded boats… I hope this helps with a few of your questions! – k