I’ve recently read that an encrypted phone is thoroughly & completely secured when first turned on until you unlock it for the first time, so it will be unreadable to any three-letter agency no matter what tricks they have unless they have the unlock code (which you should probably also change the night before to give the phone time to process/perpetuate the change).

This may not be true. It depends on the model of phone, version of the operating system, and other factors. Some agencies have tools to break into phones. They can break into BFU (Before First Unlock) in some situations, but not others. So I wouldn't rely on this to be correct.