Well, the problem is solved.

As suspected, there were a couple of issues contributing to the problem,
making it a bit more difficult to nail down.

The biggest problem was that the choke plate in the carb was bent to hell.
Seems someone in their infinite wisdom tried to play with the throttle while
they had a screwdriver stuck down the carb to keep the butterflies open.

The fuel filter / pump werefull of varnished fuel. So, although I drained
the tank and added fresh fuel, there is enough capacity in the lines,
filter, and carb to cause considerable grief on initial startup.

So, a rebuilt carb, an impeller kit, and a new battery has me ready for the
summer.

Total cost so far, including the initial price of the boat and trailer:
1844.00

I don't think I am upside down yet for a 1987 Rinker V19 Cuddy...