geez. You're not well, thompson.

That's a good engineering question, and I'll bet somebody here knows specifically how much per minute, and will provide a citation.
great historical question too -- gave us those mudflats motors and air cooled outboards, presumably. Some air cooled motors also had an impeller that I think was used to cool the leg/exhaust housing -- idea (yours) would be to use a fabricated water cooled system instead of air cooling the powerhead.
I'm guessing a gallon a minute for a 6 hp (trying to picture how much would be pumped up through the water tube if left open). And maybe that's way off. I would think simplistically of cutting/disconnecting the water tube between the impeller and the powerhead, and installing an inlet in the water jacket or maybe in the exhaust housing cover on the powerhead, or both -- then running tubing from a pump mounted on the stern of the boat to the inlet. Let the plumbing otherwise stay in place for exhausting the water. Maybe the existing impeller could be used to cool the exhaust housing, but would have to be more hardy than the rubber ones or the sand would eat it up.
??