Specific payment option - pay later after shipping estimated

My customer ships their products by truck. The first 30 miles are free. Then after that they charge $3.50 per loaded mile.

However they need to calculate the shipping cost AFTER the client has placed an order. I need to know if there is a way for the process to go like this:
1. Customer selects product
2. Checks out and submits order but doesn't pay
3. Client gets order & estimates shipping
4. Client goes into order, adds shipping cost and sends final invoice to customer
5. Customer pays
6. Client receives payment & processes order

We also want to allow a local pickup option. So people can order and then pick it up.

First of all Is this possible in HikaShop?
If it IS possible then how do I go about setting this up?

This is critical to their ecommerce solution we choose

This site works similar to what my client is looking for:
www.jimmys-cypress.com/OurProducts.aspx