Adjusting order totals after initial order

I have a client who needs to adjust an order's totals after products in the order is weighed.

So let's say a customer orders a 5 pound bag of some goods @ $3 a pound, totaling $15.

Staff weighs out a bag but it comes in at 5.5 pounds, so now the order total will be $16.50.

This variance in product weight will always happen and cannot be avoided.

Client would like to have the customer confirm the order, then charge the order total at that time.

I'm comfortable adding custom code to accomplish this, just trying to get an idea of the overall workflow.

Any insight would be greatly appreciated!

In the checkout only allow payment method Payments.CheckMoneyOrder and rename it "Order subject to weight"

Then when you do the weighing adjust the order totals

Then from their account orders page add "a make payment" button that goes to a new page with an option where they can select the payment method and make the payment.
Send them a link to the option in an email detailing the correct price