Well, I finally have a hypothesis about what is happening and to share and what looks to be a solution.
I brought the pump home, bought some clear tubing so I could see where water was (or was not) flowing, made a tool to drive the pump with my drill, then began to play. When pulling on air (i.e. startup) the pump can't create enough vacuum to pull the water column up unless I really get the RPMs up. If I can get to a point where all of the air in the pump chamber has been removed then it pumps, but clearing it of air isn't happening readily. My first suspicion was the seals to the outside - O-ring on the one side, and paper gasket on the other. But there are no leaks there. However while playing around I noticed that water inserted at the input barb leaks out the output barb, and vice versa. That suggests a leak within the pump chamber that would act as a "short circuit" between input and output when pulling on air. I confirmed the leak by getting the chamber filled and then, with hoses attached, adding water to input or the output hose - in each case the added water flows through the pump to equilibrate the levels in the hoses.
There is no obvious damage in the chamber to account for the leak - my best guess is that over the years the metal at the bottom of the chamber has been worn away just enough that the chamber is now slightly wider than the impellor. In fact, if I remove the O-ring the ability of the pump to lift water improves somewhat.
That gave me an idea. The pump has been installed on the engine oriented such that the input and output are at the bottom. If water falls out of the input tube when heeled over then the chamber becomes filled with air. And with the through hull back in the water, the short circuit prevents the pump from pulling up water. But if I re-orient the pump so that input/output are at the top, then I should be able to keep the chamber filled with water. And since water is much more viscous than air, then what is a short circuit within the pump for air may not be a short circuit for water (recall that once filled with water, the pump actually pumps). I re-oriented the pump on the bench and found that I can in fact pull water up the input hose that is initially filled with air, even at very low pump RPMs. And once that air column is removed the pump flows water to the output as it should.
I could try to remove some material from chamber to make it narrower, but since the pump seems to be flowing adequately in the new orientation, I think I'll try that first rather than risk damaging the pump. I have room on the front of the engine to re-orient the pump. Longer term I may need to remove material (or buy a new pump) if the gap within the chamber increases to a point where the gap is acting as too much of a short circuit even for water, but I expect that is a good many years away - probably the pump will fail before then at the seals surrounding the rotating parts.
Thank you to all of you for the helpful suggestions.