@ChrisSinFL

Let's do this the easy way

You charge customers for shipping, that is income, create a service item called pre-paid shipping and select an income account for it to post to, I create an income account called pre-paid shipping and use that item on your invoice.

You pay for shipping to ship to the customer, that is an expense, it is not COGS, just pay the cost and post the expense to an expense account called something like outbound shipping expense.

On the P&L it is easy to look at pre-paid shipping income and compare that to outbound shipping expense to see how you are doing in that regard

Inbound shipping for inventory items, is part of the item cost.  On the item tab in desktop list the inventory item, the qty, and click in the total cost block and enter the total cost of the item plus a portion of the inbound shipping, when you click or tab out of the block QB will do the per item rate for you.

IRS Pub 538 Page 18 which says
For Merchandise purchased during the year, cost means the invoice price minus appropriate discount plus transportation or other charges incurred in acquiring the goods. You must reduce the cost of inventory by a trade (or quantity) discount.