I believe this might be true for you now because you already have some history with Shopvox. Imagine a new hire with no sign industry experience. Although they might have worked for Boeing which uses the same methodology as Shopvox, I venture to say there might still be quite a learning curve for them.
Yes. Grossly inefficient interface and I don't believe the interface designer is at fault. Maybe you suggest they readdress their "user experience."
Seems they have you bamboozled by their terms. It may help to consider the components as just layers to make up the line item. For example; a layer of SAV, a layer of lam, a layer of substrate, a layer of edge trim, and possibly a layer of packaging material / time. All of those layers might be saved as a particular product especially if all same materials were used often in the same fashion. It might be saved something such as "Quick Print Special" where the only variables for this particular product would be the size, the quantity, and possibly double-sided next time. Who knows or who cares if any of these components are called parts or modifiers or wingdings? They are simply resources of materials, machines, or labor.
Did they ever suggest to you to create separate spreadsheets of your suppliers, materials, and products before attempting to enter "parts" and "modifiers"? If this exercise is successful, it paints a clear picture of what's necessary and then the same data can be uploaded (I would expect) to the appropriate database. These same spreadsheets are helpful to explain to new users what's happing behind the scenes of the web interface.
I hope this helps.