I'd like to be able to create an avy by making character & dress selections, as is done on Hero Forge for miniatures, or setting up characters in Bethesda video games.

This gets in the way of the hand drawn aspect. I think at best it would be layers, you have a hand drawn layer, there may be other layers you can select/add some visuals to, certain trophies or cosmetic items in your inventory alongside your avatar. A colored filter. Some effect that when clicked can transform your avatar in a small way, interacting with them and they respond in a sense.