Planning a road trip to Yellowstone from Los Angeles

I'm planning a possible end of summer road trip to Yellowstone from L.A. I'm sure many people here have made this trip or a similar one coming from another area. I have about 10-13 days. Here's what I was thinking:
1. Taking the 15 freeway Northbound from L.A. First stop Hurricane, UT. KOA (6 hours)
2. Provo, UT. Lakeside RV Campground (3.5 hours)
3. West Yellowstone. KOA or Rustic Wagon Campground (5.5 hours)
4. Yellowstone -Madison Campground
5. Yellowstone -Mammoth Campground
6. Yellowstone -Tower Fall Campground
7. Yellowstone -Grant Village Campground
8 Grand Teton (Anyone know a campground here)?
9. Salt Lake City - KOA
10. Zion - Watchman Campground
11. Travel back home to Los Angeles
I don't know if it's too late to book these campgrounds, but I'm just doing the research now. Does anyone have any advice? I've planned to travel each day. Is this a good idea or should I switch things up a little and stay at some places for two nights?
And or should I add a night or two at a hotel to freshen up?
Thanks.
Scott
1. Taking the 15 freeway Northbound from L.A. First stop Hurricane, UT. KOA (6 hours)
2. Provo, UT. Lakeside RV Campground (3.5 hours)
3. West Yellowstone. KOA or Rustic Wagon Campground (5.5 hours)
4. Yellowstone -Madison Campground
5. Yellowstone -Mammoth Campground
6. Yellowstone -Tower Fall Campground
7. Yellowstone -Grant Village Campground
8 Grand Teton (Anyone know a campground here)?
9. Salt Lake City - KOA
10. Zion - Watchman Campground
11. Travel back home to Los Angeles
I don't know if it's too late to book these campgrounds, but I'm just doing the research now. Does anyone have any advice? I've planned to travel each day. Is this a good idea or should I switch things up a little and stay at some places for two nights?
And or should I add a night or two at a hotel to freshen up?
Thanks.
Scott