I've been to a bunch of places like this; offshore islands. If you reboot your phone, you will be able to make calls. I think the phones get re-associated with towers that aren't going to work (perhaps for the distance/timing limitations) because they have a strong signal, and stay connected with those towers, even though it's not a good functional choice.
Some phones allow you to force the phone to roam as well, which could get you some more options.
Amateur radio is the most foolproof option. Simplest infrastructure, longest range.
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