What you removed from eCart was the shipping charge rule, the USPS shipping quote server behavior is still intact on the confirm page and will need to be removed. On the confirm page look for the shipping quote server behavior in the list of server behavior and remove it.
For the new rule you can just add one in. For the trigger use 'number of items in the cart > 0' and for the calculation choose based on a column subtotal and use the quantity column, then choose 'times' and enter the amount per item you would like to charge for the shipping.