What do you mean? The DMG has a whole section on "nonmagical" diseases that incredible things. Sewer fever, and some kind of brain malady that gives you insanity and spreads when you sneeze, IIRC. Clearly "nonmagical" doesn't mean "realistic."
A simple fix for Contagion is to just say that you can spread any disease which actually exists in your campaign world, but that the diseases in the PHB are just examples and don't necessarily exist. Then make up four or five diseases that a PC can learn via Medicine check or actual exposure, and voila, Bob's your uncle!
I do, however, use the same rule you do w/rt "successful save = not affected for that round." Your Rotting Flesh symtoms can come and go while the spell is trying to forcibly impose the disease on your body--but at the end of five rounds, one side or the other has the upper hand and at that point, the disease is either gone or will run its course normally. The PHB is pretty unclear on whether that's how the spell is supposed to work but it seems reasonable to me.
I saw the small section in the DMG. It didn't say much more than "It's up to you."
I'll probably run contagion similar to how you're doing it with the addition that the spell has no effect on undead or constructs. A powerful divine disease that affects all types of living creatures fits well with what I want. If I want a disease that affects undead or constructs, I'll make something else up.