UPDATE!
I know this is long winded, but please be patient.
I took all the fuel out of the tank, and dried it out the best I could with old rags. Then I put in fresh fuel(Again) with a generous amount of "Seafoam". I took off the fuel lines, and blew carb cleaner through them with the air hose.
I removed the carb. to make sure of it one more time.
I removed the filter, and put it in carb cleaner. Put carb cleaner and them seafoam in fuel lines, and blew them completely through the fitting. every thing was nice and clear. Reinstalled carb (without the filter). I filled a garbage can with water to use as a test tank. When I pumped up the tank, I could see really clean fuel in the bowl. It started well, and ran well. I could put it in gear, and could get a bit of speed.
Every thing was working well, so this morning I decided to put it in the water for one more try. Everything worked great. Forward, and reverse, and up to speed. I ran it for about a half hour at various speeds. Until I ran out of fuel. I didn't want to make up too much this late in the season.
I think I have got it cured.
I am having trouble finding a filter and gasket for the sediment bowl, so if anyone can direct me, I'd appreciate it. I am going to let the old one soak, and hope for the best.
Has anyone ever used an in-line filter on one of these old motors, instead of the bowl one?
Just a thought.
I want to thank you guys for all the help, and suggestions through all of this. It was very helpful, and encouraging.
P.S. I'm glad it didn't turn out to be that "shock absorber" thing.