I'd like to control what currencies a customer can view and buy in on a customer by customer basis. Is it possible to force a customer to only be able to use one currency?
You would need a base currency per store and redirect them to it, if you have many products and many currencies you will need a lot of server resources.
That does not include the maintenance of keeping the products in the base currency per store.
If it is just the display currency then there are various extensions or you can have it coded.