A couple thoughts for you:
1) On my Cub setting the float height did not give me the correct fuel level, I ended up actually measuring the level to get the correct float height. It takes a hose barb in the bowl drain hole and a piece of clear tubing. To compound your potential problem there are apparently some Cub kits floating around that have the wrong float height in the instructions.
2) It's normal for an updraft intake to spill some fuel when starting, particularly in cold weather. Your Cub has a drain near the choke butterfly to dump that fuel. If the tractor doesn't start for any reason it will dump enough fuel to be easily confused with a flooded float bowl.
Re-reading your post it appears that the gas doesn't run out until you crank it with choke. That sounds like #2 above.
The reason I was measuring the fuel level in my Cub was because it was almost impossible to start hot. After chasing a lot of things it turned out the carburetor was not my problem. In hindsight it seems the Cub is tolerant of a wide range of fuel levels. If it's not spilling fuel until you crank it you should probably be looking for a different cause.
