I know this is an old thread and you've been given practically every solution possible, but I didn't see anything mentioned about a defective or lack of a thermostat. Heat exchangers do sometimes fail, not regularly, but thermostats do. Was it taken out? You didn't mention the temperature your boat operates while under motor. That's the first thing I'd look at to see if there's a problem.
"I realize the instant one would only be good at the dock. What I'm wondering, is if I really need one at all."
Please, for the sake and sanity of crew, get one, any one