Edit Customer's Shopping Cart

I have a customer that is out of my usual shipping area whereby I'd like to be able to add a shipping surcharge and also change the contents of the cart if need be.

I think the ideal would be if the customer were to put stuff in the cart and then abandon it. I would then convert it to an order and do whatever other edits were needed.

The customer would then log into his account and complete the transaction with a credit card.

Is this possible? Is there any other workaround that would serve the purpose?

Create the order using the customer's account and leave it in Open status. Make sure in Order statuses that the 'Pay order again' is checked for the Open status. The customer can then log in and select the order and complete the transaction.

we use this from simtech but there are others

https://marketplace.cs-cart.com/cart-sharing.html