to add multiple items at a time, you will need to use a dynamic cart.
There is not going to be a supported way to accomplish what you are trying to do, which is to add one item to the cart that is treated like multiple items by the UPS shipping rate calculator.
Whether you approach from the stand point of adding multiple items to the cart with one add to cart button or one item in the cart that gets treated as many, eCart is not designed to work that way and will require hand coding of the PHP.
I think you will be better off calculating the shipping in another way rather than using the rate lookup service.