Just to finish this project out:
I figured out a way to get only the white portions of the badges changed to black. First, I spray painted over both the badges, exposed copper parts and all. After letting them dry, I took a shop towel and dabbed it in some xylol from the hardware store. I then wiped off the raised (copper) parts with the xylol-ed shop towel. I only messed up a couple of times when I got too much of the solvent on the shop towel and it ran down onto the parts I still wanted painted black. They look alright from about 6 feet away, but you can see that they’re not quite right up close.
Still on the hunt for some original black badges that look like these if anyone’s got a line on them...