Would it be okay to wash and thoroughly dry the potatoes then store them for long periods of time then rewash them again before use?

It’s best to store potatoes as-is from the consumer bag you purchased them in and keep in a cool (not cold) dark and dry area. Such as in a pantry or cupboard. Use within a few days, as potatoes will continue to dehydrate, sprout and are subject to skin greening. Before using, that’s the time to rinse the potatoes with clean water and prepare as desired.