I was wondering the same thing about flying from SLC to DIA... If you went to Moab and explored Arches/Canyonlands, the drive to Rocky Mountain NP would only be about 5 1/2 hours. Rather than driving four hours back to Salt Lake, checking into the airport, a 90-minute flight to Denver, renting another car, and then another 90-minute drive to RMNP. There are always rental drop fees to consider, I suppose.
I would say, if you are already going to Rocky Mountain NP then for a contrast, head down to the desert in Southern Utah. It's a different planet and sure to please. You could spend a couple of days in Salt Lake/Park City and the Wasatch Mountains, which will be starting to change autumn colors, and then head to Moab for the rest of your time before RMNP. If you really wanted to see bison, there is a herd at Antelope Island in the Great Salt Lake, one hour from downtown SLC. It's not the same as Yellowstone, but it could fulfill seeing some wildlife.
There is great whitewater rafting on the Colorado River. Westwater Canyon, the Onion Creek float trip, or the rugged Cataract Canyon can all be accessed from Moab. By September the water will be much lower, but I've been in November and there are still big rapids and there is always beautiful scenery. It's actually a fantastic way to view the towering cliffs, mesas, and canyon walls. I love being on the water.
It would be the perfect time of the year to camp in the desert. The days won't be unbearably hot, and it will still be warm enough at night to be comfortable and look at the stars. Bring layers. You could visit Arches and both, Island In The Sky and The Needles sections of Canyonlands. Capitol Reef is about 2 1/2 hours from Arches and cold be worked in there too, on the way back to SLC, if you decide to do that. I agree not to try to squeeze too much in. Either visit Zion/Bryce or Arches/Canyonlands and you could throw Capitol Reef in with either.