Is it an option to create the bags without the clear window/wing insert for pins? Just have a solid black leather (or whatever material it is) wing? Hope that makes sense!
All of the bags will still have the window so it will still be kind of shiny there, but you can leave the insert blank for a less busy looking bag! I don't have anything that would cover the window at the moment.
also in case anyone was wondering - the wing inserts are a sort of satin material over a thin piece of foam