Yes, it's all very strange, lol. Well, treating for mites won't hurt! Instead of gasoline, go for the Vaseline method which literally smothers them to death (so it shouldn't take weeks) and has the added effect of helping moisturize and remove dead scales so new ones can grow, or you could try the Eprinex or the mite specific spray Rancher recommended. I just really wouldn't use gasoline. It might be on that page but it's definitely an old timey treatment that's not recommended anymore like how you really shouldn't go splashing it all over a dog to try to treat mange.
You know, the other thing that has me questioning mites is the smell. Can't imagine mites would smell like that.