epsom salt is some good stuff but I'm not sure it'll do what your asking , sure won't hurt to try.
Salt is a natural antibacterial, but like you, I don't know that it will get into the skin enough to do the job. Maybe if King showers first & scrubs his back with soap to remove dead shin & oil, then the salt will penetrate better.
Aveno , does a good job on sensitive skin and they make several products , you may want to check into those.
Aveno is great stuff! It's the only thing my doc recomended for my baby when he was born. Vasolene on his ass & Aveno everywhere else. (except his lips/mouth)
A company called Melaluca makes several products with tea tree oil , thats pretty good stuff and has alot of uses
Tea tree oil is good, but VERY STRONG. As in, it can cause painful, itchy rashes. Maybe diluting it down to a 5%-10% concentration in some cooking oil might tame it to a useful potency.
Personaly I'd contact Emric here on the board and see what he may have an idea on
Yeah, Emeric might have something to say about fighting AAS acne.