SLC is at least a 5 1/2 hour drive from Jackson. Half the time, the road you're on is a two-laner. I used to live at the halfway mark.
The airfare up to this neck of the woods is horrible- it's the same going out from here to anywhere, too
. I say, pay the money to fly into Bozeman and take the Gallatin Canyon to West Yellowstone or fly into Billings and take the Beartooth Highway out of Red Lodge to Cooke City. Spend your first night in one of these three towns. The second route has been voted one of the most scenic highways in the US. It has to be seen to be believed. You could make a loop out of this drive as you go through the Park.
I think what you have planned is pretty good, although I wouldn't spend as much time at Lake, I don't know why. I'm not a fisherman, and it seems like the good wildlife watching, sights and hiking are not at Lake. Wildlife is great in the Lamar Valley and up over the pass on Mt. Washburn. Like Disney World, you have to get up early to beat the crowds and see the "shows"! Head for the hikes in the p.m. to avoid the crowds, but always take a rain jacket. Rain at this altitude is dangerous.
If you want to try "roughing" it I would highly recommend the Roosevelt Lodge, or the cabins at Mammoth or Lake. I always feel more out in nature in those cabins. It's a short walk to the bathrooms, but not being in a hotel is kind of neat. My favorite is Roosevelt. There are NO crowds there. Ever. These cabins are cheap and will make up for your high airfare.
Also, I went the first week of Sept. last year and was stunned by the amount of people. The rangers at Norris Ranger Station said that young retirees keep them hopping all through the autumn. It wasn't like July, by any means, but it was busy. You will not have the place to yourself, sadly.
Finally, if Xanterra's website doesn't show any vacancies for your stay- call them! They do not update that website very often and cancellations may not show up at all. I think Xanterra runs the lodging facilities extremely well, but their website-
not.
Have a great time! Other folks have Disney- but I have Yellowstone
!