I think you want the “Use Image” setting on the Mask trait. The non-owning player sees your generic counter image and that’s it. Set this in the upper portion of the Mask trait config: “View when masked”.
Seems like you basically want to see the unit with some minimal indicator that it is hidden to others. Wouldn’t a mostly transparent image with some text like “CONCEALED” or similar do the trick? Just size the image and place the text where it makes the most sense for you–above, below, off to the side, whatever. Perhaps I’m missing why one image can’t work for all units (assuming they’re all the same size).