I still don't under stand what is keeping the petcock from closing off. The body is in good shape but its just not closing completely.
Got to be something going on there. Some damage that you may not have seen is what comes to mind. Or a piece of debris stuck to the valve core. I'm trying to remember the design of that valve, I think that damaged (rubber) seals would allow fuel to leak outside the valve body.
But I guess it would almost have to be trash holding the valve seat open. That would explain the flooding and the fouling of the plug in number 1.
Maybe, you still haven't said if you are finding sediment in the carb bowls. If you are maybe an in-line filter might help. Many wii stop particles smaller than the screen in the tank can stop.
Have you checked the (float) needle for wear, damage or a stuck plunger?
A couple of months back, I was helping a friend get an old "400 twin" running. Among other problems the carbs were overflowing as would be expected. The plungers on the needle valves were stuck and the local Honda stealer was only too happy to provide special order replacements for a large amount of money. We installed the new needles checked them before screwing on the float bowls and put the carbs back on the bike. Fired it up and what do you know, peeing gasoline all over the floor. Upon close examination a piece of varnish was found stuck to the tip of the brand new float needle. You must study these things carefully. Removed the flake of varnish (which was soft enough to disappear when rubbed between my fingers) and overflow was gone.
Good luck