Steve, I was also going to suggest more agressive claybar also but had similiar problem with a car and claybar didn't work for me. I found that a white 3m sponge used with adhesive remover and used carefully in moderation will take off overspray without messing up the satin black. Really depends on how durable your black paint is. The standox black we use at shop will hold up to this and most of time you can get the overspray off. Any questions feel free to call me at shop.
Joe