Part Configurations vs. Toolbox Parts

I'm trying to create a library of parts, configurable when I drag them into an assembly. However, I want a little more flexibility about it than I'm seeing so far.

What I have accomplished is to create parts with different configurations (controlled by an Excel table). In this example it's a screw with a collection of configurations describing (diameter) size and lengths. I've managed to add it to my library, and when I drag it in to an assembly, I'm able to pick the configuration I want to use. I can even change it afterward. Groovy.

However, if I drag something in from the Toolbox, the behavior is much different. Instead of picking a configuration that is a specific combination of diameter/length selections, I'm able to select each of these things independently.

I've found the files for the objects in the Toolbox, and as far as I can tell they are just ordinary .sldprts, but it's not obvious to me how the various selections are defined. Even though the configuration on this example part seems to show some of the dimensions driven by the selections, I don't see any control of those lists here.

I've also found the Toolbox configuration, and it seems to show a large collection of complete configurations when seen in this view. Way more configurations than I see in the part configuration table itself.

Is there a way to define configured selections independently of one another, or have I just been tricked into thinking this capability exists because of the interface that's been offered to me? If it's the former, I'd like to be able to reduce the number of explicit configurations I need to manage. If it's the latter case, is the Toolbox something I can add items to in order to co-opt that functionality? I've seen Youtube tutorials that show parts being added to the Toolbox, but when I follow those steps I'm limited to adding to the Library, which may not offer some of these features.

 

Thanks!