To just part of your question, in some western states (Colorado and New Mexico from personal experience, but maybe others) the local power company has installed public electric chargers in some towns, sometimes at their local office, or sometimes downtown. For example we wanted to take some smaller roads from Durango to Santa Fe via Pagosa Springs, and there was no Supercharger along the route. But there was a fast charger in Pagosa, so that filled our need.
As to the time, we timed it for breakfast at a coffee shop there. It was about a 1 hour stop.
The power company in Taos (northern NM) has chargers at their office. In that case, they are slow chargers, which is a bummer, but it's walking distance to restaurants and stores and things to do, and free, and it's enough to extend the range a bit and get you on your way to the next faster charger elsewhere.
Almost everywhere there are chargers at hotels. For Teslas hotels often have Tesla connectors which are faster than the other hotel options. They often will allow you to plug in for a charge for a fee, even if you aren't a guest, on an as-needed basis in the daytime. For nighttime, I assume guests get priority.
I haven't scoped out Wyoming. We did traverse Nevada and Utah and no problem with Superchargers but were only on small roads for some of the time. I mean if you are charged up to 300 miles, you can drive for (up to) 300 miles on small roads if you know there's a charger at the other end. Obviously I would build some margin into that.
With Superchargers most stops are between 10 and 20 minutes, for me at least. Some people stay longer because they think you have to charge to full at every stop. This is wrong, and slows down your trip because topping up that last 20% gets slow, since charging slows down as you approach full charge.
I've been from California to New Mexico and back four times, to Oregon and back twice, to San Diego once, to LA and back a bunch of times, and to the far side of Texas and back once. Way more enjoyable than in my old ICE cars. On longer trips if Superchargers are spaced out wider, the stops are slightly longer just because I like to keep a margin of extra range. If there's no Supercharger then there are sometimes fast chargers at Walmart, but usually fewer of them, so if you don't have a Tesla you have way fewer options.
Major routes are very well covered. Minor routes, say going down through Ouray and Silverton, I would incorporate a hotel with a charger into my plans to charge overnight, but you should have a backup option because someone else could have occupied the hotel charger first. I don't know whether some hotels allow you to reserve a charger in advance. Haven't crossed that bridge yet but I imagine some do.
This is all a moving target though as the system is being built out rapidly. I think hotels will start catching on that they need to add more capacity soon.
The high order bit here is, and sorry for making it a company product endorsement, but if you're going to get an EV, get a Tesla. Way more options. Especially if you buy a CHAdeMO adapter (yucky, but useful). Non-Tesla drivers are going to get very familiar with Walmart, which is fine, but pretty limiting, and are probably going to be reluctant to go on road trips, pretty much the opposite of the Tesla experience.
On the other hand.
If something breaks, with a Tesla your car is going to be loaded onto a flatbed and carried far away to a Tesla Service Center somewhere, and you are not going to see it for a while! That's kind of a different topic though. They don't seem to break in such ways very often. Usually only when hit by an ICE car driver, lol. It's probably even worse with other EVs, some of which sell way smaller unit numbers, like the Kona — good luck finding service for that.