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Aren't some US post offices 24/7? You could go overly cautious and have them at 400km intervals rather than 600km and if you miss one then it's not too much of concern.
So I just calculated that I had an approximate moving time per day of 15.30 hours so maybe something closer to 17 hours including non-moving time on the bike (quick toilet stops, putting clothes on, checking navigation, quick jump into a shop).
I slept with no power source 7 out of 13 of the nights on average for about 5.5 hours and I'd stop properly twice a day for 30 minutes in restaurant/cafe/MacDonalds with charging.
However I never really went under 50% and only on a few occasions did I have to start using my reserve battery. For example the first three days I slept outside so had no prolonged charging
On the TransAm could you send off a pile of power banks say every 600km. Might get quite pricey but would solve the power/stopping anywhere for long problem.
I carried about 22,000 mha of power on TCR and rarely went below half as when I'd stop I'd stick my batteries, phone and garmin immediately into a charger.
Edit: that being said I've just got a dynamo..