Keep the field based on Parts::Product_ID.
Make the drop down's value list a two column value list. Make column 1 Products::Product_ID and column 2 Products::Product_Name.
Then, when you select a product, you can use the name to select the correct one, but the drop down enters the ID. Parts::Part_Name can be set up with a looked up value setting to copy the Products::Product_Name into it each time you select a Product ID.