We were 31 year residents of Estes Park and guides in RMNP. Kind of know the place. There is absolutely NOTHING available as you described in RMNP or Estes Park. The quietest campground is perhaps Estes Park Campground at East Portal. Moraine Park and Aspenglenn campgrounds are in a beautiful setting, but you will have to listen to generators in not quite hours. Go to the RMNP website for more information.
Mid September is prime leaf color time and elk rut. September is almost as busy as summer prime time.
The solitude you seek is available not far from the maddening crowd in RMNP, but you will have to find it. 95% of RMNP is designated wilderness and probably 95% of the people are crammed into 5% of the Park. You will not find a wilderness experience in a campground in the Park, but you can find wilderness near those campgrounds by getting off the beaten path.
We love RMNP with all our heart and soul. The wife's family started vacationing there in 1917, and I married the place in 1974.PM me with contact information and maybe I can help you.