Tax based on Product rather than address?

I know this sounds a little strange, but...

We rent products to students of specific schools, and then deliver all products ordered for a particular school in one truck. The sales tax does not depend on customer's billing address (could be a parent living in a different state or country), nor our store's address, and we don't use shipping address, as only certain products are available for certain schools and/or residence halls and we don't want someone ordering for a particular residence hall if that residence hall isn't on the approved list - which using the shipping address could allow.

So, in short, we set up schools as categories, approved residence halls as sub-categories, and the products under that. We then set up various tax classes and rates, selected the appropriate class for each product, set tax basis to "store", and set price to display without tax. And everything worked great! Product showed the net price, and when we checked out, the appropriate sales tax (based on the product, not billing or store address) was properly calculated and added. Everything seemed perfect - until the client informed me that the net prices were actually the gross prices (i.e. they included the sales tax already)!

OK, I thought, no problem, just have to set price to display WITH tax, change all product net prices, and done. I wish...

Now, the price displayed on product page is the gross price (which is what we want), but only when not logged in. As soon as I log in as a customer, the displayed price changes to the net (doesn't matter what state is listed in customer's billing address), and checkout does not work right (and worse, works differently depending on the state listed in billing address). What happened?

I know this is confusing, but does anyone have any ideas on how to make this work?

I would be most grateful!