Hi Kent,
I took similar trips to Mt and Idaho in the past. I went eleven summers in a row for the entire summer from late May through late August. I took various routes to get to the West Yellowstone area. Stayed at the Campfire Lodge along the Madison below the Hebken Lake dam. While it was my base of operations for the summer I went to many places in Western Montana and Idaho.
There are lots of places to get you side tracked. I am going to share with you a less traveled path that I experienced in various forms many times when I went North from Tucson.
I figure you would not want to camp anywhere with the heat. First practical place to stay for the night would be near Jacobs Lake. The route is across Marble canyon bridge, past House Rock then up to the plateau near Jacob's Lake. I have camped for the night on many of the small pullouts along the road.
When you well past Kanab and are going North on Hwy 89 you could visit Panguitch Lake which is 18 miles from Panguitch. It is 8200 ft elevation so you would have some cool camping weather.
https://www.fs.usda.gov/recarea/dixie/recarea/?recid=71021Or you could skip Panguitch and go to Fish Lake instead. Elevation is 8848 ft. Lake is 6 miles long and 1 mile wide. Fish Lake holds rainbow trout, splake, lake trout, kokanee salmon, brown trout, tiger trout and yellow perch. Yellow perch are regarded as an invasive species; there is no bag limit and anglers are encouraged to dispose of any yellow perch caught.
https://en.wikipedia.org/wiki/Fish_Lake_(Utah)
From Fish Lake, IMO, you should take the less traveled route which takes you through Price Utah. A Columbian mammoth was discovered in nearby Huntington and the museum was built around a replica.
Within the museum is the little known Utahraptor. which is the largest-known member of the family Dromaeosauridae. Its large size and variety of unique features have earned it attention in both pop culture and the scientific community. The jaws of Utahraptor were lined with small, serrated teeth that were used in conjunction with a large "killing claw" on its second toe to dispatch its prey. Its skull was boxy and elongated, akin to Dromaeosaurus and Velociraptor.
https://www.southwestbrowneyes.com/2015/04/discover-prehistoric-museum-in-price.htmlFrom Price you can visit Vernal which is a dinosaur mecca with another small museum and tons of curios shops.....
My favorite item I picked up there is a large rock like object which represents a dinosaur egg with a portion of the shell cracked open with two eyes looking at you! My wife had her birthday when we visited Vernal and she loved the gift, so did her students as it was used as a paperweight....
You could visit the Dinosaur National Monument or skip it and go directly to Flaming Gorge Reservoir. It is a large lake which is mostly in Wyoming, elevation a bit over 6000 ft. It has many dirt roads that lead to primitive camping on the North end of the lake, off of highway 530. Fishing is varied with rainbow and lake trout, it also if famous for its large Kokanee salmon. There are smallmouth bass too. I fished it on many occasions targeting the kokanee with downriggers. If you go there you can expect it to be windy. The North end where it is narrower would be where I would use the kayak.
Drive North to Green River then go a bit West to the next destination, Bear Lake. The clear blue water just has to be seen! While I had not been to the East side in a long time, I primitive camped on that side. Catching fish would be difficult as there are mostly cutthroat trout which are found deep in the waters due to its clarity. When you drive out on the West side, to go north, be sure to stop at one of the places that make a raspberry milkshake! The highest rated ones being La Beau's or Chevon.
At this point you can get back on your original route to Montana going to Pocatello and North or take the other route toward Gran Teton and Yellowstone National Parks. If you have never seen them, I recommend the parks. Camping will not be pleasant but those places are a must see.
Should you go through the parks.....Once out of Yellowstone and into the city of West Yellowstone take route 191 North and turn left on 187 towards Ennis, which was mentioned by another poster. 187 goes along Hebken Lake. It is famous for its "gulpers" rainbows that eat insects that are on the surface. I have trolled it extensively and caught many rainbows and browns using a rainbow or bright orange F7 floating Rapala. Browns will go after a lure that is being trolled at some very fast speeds. So if you decide to give this lake a try there are many places to launch your kayak. Unfortunately this whole area does not allow primitive camping. The forest service wants your money.
If you are considering staying in the area I would suggest Beaver Creek Campground. Just down the road a bit is Earthquake lake. More on that below.
You could also stop at the Campfire Lodge for a great breakfast or lunch. If you do, sit in the outer room overlooking the Madison!
If you pass on Hebken be sure to check out Earthquake Lake. It was formed when 100 million tons of rock slid off a mountain in 1959 blocking the Madison river. It is not built up at all and the only launch ramp is just a dirt road leading into the lake. It also has trout and is the perfect place for your kayak. Beaver Creek Campground is less than a mile away.
https://www.recreation.gov/camping/campgrounds/233181Once you leave the lakes and are traveling towards Ennis turn off at the McAtee bridge, cross the Madison River and drive deeply into the Wall Creek Elk Reserve. The drive will take you uphill and on to a vast pastureland, the elk preserve is a wintering ground. Hunting is allowed there. In fact near the river in boulder fields you will find marmots. You may hear them chirping at you but may have to glass them up. Shots are usually more than 200 yds. You could camp in there and shoot ground squirrels till you burn out. As a local Sheriff once said, " there are lots of them in there that need murdering". My best day was 180 in 3 hours with my 10/22.
At this point I would say drive to your final destination which looks like the Missoula area.
Should you decide to go a bit more north to the Kalispell area there are many lakes in the area. I fished Flathead on several occasions and caught many huge lake trout. Also fished Swan Lake for one day where I caught a couple of Dolly Varden trout, oh excuse me, they are now called the unglamorous name Bull trout.
https://itiswild.com/best-lakes-near-kalispell/Should you decide to visit Northern Idaho you must see Lake Pend Oreille! I camped at the Garfield Bay Forest Service campground in June and was totally alone up there! The bay is isolated from potential winds and waves you can encounter on this huge glacier made lake. It is famous for its huge Kamloops rainbows but does have a population of kokanee. It does have quite a few species of fish: Largemouth Bass, Smallmouth Bass, Rainbow Trout, Cutthroat Trout, Kokanee Salmon, Brown Trout, Lake Trout, Walleye, Northern Pike, Black Crappie, Bluegill, Pumpkinseed Sunfish and Yellow Perch. Pend Oreille Lake is known for its huge kamloops rainbows. The largest I caught was a 37" on a lyman plug trolled 70 ft down with down riggers.
There are some small lakes in Northern Idaho which I didn't visit. I did go to Priest Lake for giant lake trout. That is a dangerous drive with loggers on a narrow road not recommended for faint of heart.
Well Kent, you asked for some ideas. Hope you have a great time where ever you go.
Ross