How can I plan a cross-country EV trip with spotty charger reliability?

[AndrewKL]

I'm planning a cross-country road trip in my new electric vehicle next summer and am starting to map out the route, but I'm concerned about the reliability and availability of fast charging stations, especially through more rural stretches in the mountain states. I've used the popular apps, but real-time status on charger functionality seems hit or miss. For experienced EV travelers, what tools or strategies do you use to plan a long-distance route with confidence, and how do you handle contingencies when a planned charger is out of service or has a long wait?