Hello Strikebox,
Welcome to the Community page,
So it is not possible to do this in Quickbooks. The expense category is on the cost of the product and will never show in the product/service drop-down. the product and service will show the name of the product ect never the expense category as the category is with in the set up of the product. You would need to run a report to show that detail, such as balance sheet would have the expense categories on.