EAM Work Order Billing - Invoicing for Hours Worked

I need to invoice my customer for the total hours worked on a Work Order times the hourly rate defined in the EAM resource.  How do I do this?

I do not want to use a price list because I want to use the item costs (for the materials used on the Work Order), and I want to use the hours charged against the Work Order times the hourly rate defined in the resource screen when I click on "Rates."

I have followed instructions on how to setup an Item and associate that item to the EAM Resource, but the item's cost is always zero and never seems to get updated based on the work order that is completed.