I've never tried using fuel stabilizer as a corrosion inhibitor or lubricant but if you think the stuff you have is capable of that, it's probably all you need. I use TCW-3 non-synthetic outboard oil to "fog" my Seadoo b/c I have tons of it lying around anyway, I fog everything with it and it's designed for a marine environment. Works for me just fine so far, even dry door hinges like it.
One negative about being too aggressive with fogging is plug fouling can become an issue.
Outboard and outdrives use an neoprene impeller in their fresh water cooling pump, one crank off and the impeller is torn to shreads in 1 second. Not so with a jet, the cooling water comes from a pressure tap at the stainless jet pump impeller. I can't recall the last time I connected a hose to mine, just don't overheat the exhaust system, if that's getting hot something else probably is too.
It's easy to fill/flood a jet ski exhaust system with water from a hose, this enters the cylinder ports if the engine isn't producing exhaust pressure to blow the cooling water out the exhaust. Outboards and stren drives are much lass susceptable to this as their exhaust pretty much goes straight down and out (no post nazi's, I'm not down and out, lol) as opposed to horizontally like in a jet ski