I'd compromise and go with Joshua Slakes. As you mentioned, DaddyBoyJosh does carry the age dynamics plus there are plenty of guys who don't think of themselves as "daddy" and/or do not get into "daddy/son" play. "DaddyBoy" anything also has a short shelf life. At some point you will age out of that and then what? Re-brand AGAIN?
My concern with Jonah is two-fold: First, it breaks from your existing name Joshua. Second, Jonah is popular now but will wane in the next few years. Joshua is a classic name but is different than John or Bill or some such.