Also, when baked we will store some in Styrofoam boxes and they continue to bake causing over cooking.  Do you have any suggestions how to prevent this and keep the potatoes hot?

First off, I’d like to say thank you for using Idaho® Potatoes for your event.   The food safety issues with potatoes come up when holding potatoes in a middle zone of not too hot, not too cold once they are cooked.  So, as long as the raw potatoes you wash are being stored properly, go ahead and wash them on Wednesday and bake on Friday.  Just don't coat the raw potatoes in oil or butter and then put into foil.

In foodservice we don't recommend wrapping the potatoes in foil for preparation.  It steams the potato when cooked as the moisture cannot escape (a potato is typically 80% water so you are trapping it inside) and the outer skin will be wet with an interior flesh that is soggy.  Potatoes actually take longer to cook when wrapped in foil as the aluminum has to be heated up before the potato inside will start to bake.

Here is what I recommend... to have a hot potato that is dry and fluffy, as well as being able to store the potato in foil for an extended serving time, bake the potatoes on Friday AM (for service at lunch time) without any foil.  Once the internal temp is 185°F or more (210°F is ideal) pull the potatoes from the oven, and with one person using a mitt, hand the hot potato to another to wrap in foil.  You can achieve a superior tasting potato.  Pre-heat plastic coolers with hot water and drain the water just before placing the foil wrapped potatoes inside.  They will keep warm for the serving period.  Give it a try and I think you will be getting "compliments to the chef".