Let's start with Wyoming:
1. You need to use caution coming into Wyoming over Teton Pass - it is steep with fairly heavy traffic and so-so shoulders.
Because Jackson is so expensive, ordinary folks
commute over Teton Pass - unbelievable! So morning and late afternoon are bad.
2. Are you staying at Spring Creek on top of East Gros Ventre Butte? Or did you just click in the wrong place?
Spring Gulch Road is actually a quiet way to head north - short unpaved section - but you miss any services in Jackson.
There is a bike trail from Jackson all the way into Grand Teton N.P.
3. Do you really aim to ride Antelope Flats Road on the east side of the park?
The bike trail takes you right to Jenny Lake where there is hiker/biker camping.
You can ride the wrong way on Jenny Lake Road - plus you should do a short walk for the views around String Lake.
4. In Yellowstone - You cannot ride on the long-closed trail you marked. You can ride along the lake and on Gull Point Road.
But why not take the lower loop from West Thumb to Madison, Norris, Canyon, and Fishing Bridge?
I mean, Old Faithful is a zoo, but the Firehole River and Norris and esp. the Canyon & Falls are fabulous.
5. Heading east out of the park - just stay on US 14/16/20 all the way to Cody.
There is a grizzly zone for forty miles from Fishing Bridge east with no tent camping.
6. You can take WY 30 thru Burlington (cafe/store/ask to camp) to Basin - much quieter.
7. Orchard Bench Rd south of Basin is a nice choice.
8. Do You really want to take the old, dirt highway up Tensleep Canyon?
It is reasonable, maybe a bit more shade, and has almost zero traffic if you are climbing slowly.
Also, they are doing construction on the main highway this summer.
9. Crazy Woman Canyon is spectacular but can be really muddy in spring. (Klondike Rd., too)
Staying on US 16 gives you those magical wildflower meadows in late June.
10. And stay on US 16 thru Buffalo - maybe checking out the little historic downtown.
11. What's the squiggle east of Arvada?
12. Stay on US 14/16 thru Gillette for services - then to WY 51.
13. What are you doing between Rozet and Moorcroft? Stay on US 14 thru Moorcroft - Donna's Cafe.
14. What are you doing around Keyhole Res? Stay on US 14 to Devils Tower Jct - some big hills.
Ripoff stores next to Devils Tower - Hulett is a nice country town.
Pic - Tensleep Canyon

14.