Free shipping on some products but not storewide.

No it's not possible unless you modify the code of the shipping plugins to handle that.

It would be if you wouldn't need the weight or the dimensions of the products for the shipping fees calculations. So you would set a volume of 0 for all these "free shipping" products and then have a specific shipping method with a price of 0 which would also have a max volume of 0.01 and then set a minimum volume in other shipping methods. But since you're using UPS and USPS to calculate shipping dynamically you won't be able to do that as they require both weight and dimensions for the rates calculations.