Tax problems with promotions and free products

I have a “promotion” (coupon code) set up that gives the customer a free product and free shipping. (Basically the coupon discounts the price of the product by 100% and also gives free shipping)

However, the customer will still be charged tax for the item. I would like the product to be 100% free. Is this possible?

It seems to work if I check the “price included in tax” option, however, I charge tax based on shipping location. So in order for this to work I would need to set different prices based on location I think. Again, is this possible?