As far as I know there is no "inexpensive" option available. When it comes to taxes every one is trying to make (more than) their share.
As for the zips not matching county lines, check with your state tax commission for their recommendations. At least some states allow for the tax to be what you charge at your local establishment and not what is in affect in some other place in the state. In that case it wouldn't matter where the item was going in the state the rate would be your local rate.