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Is it possible to have the float (tang) barely touch the spring loaded plunger tip while freely hanging on its pivot?
Yes - this is right where you want the float to be when measuring float height (notice I added the word 'tang').
This will almost certainly NOT happen with the carb body exactly "vertical", which is only a rough guideline word provided by a Japanese shop manual writer with limited English proficiency.
If you can't stop the flow of fuel no matter what you do, there's a problem in the float valve area for sure - it could be a leaky valve, leaky O-ring, cracked carb body, loose hold-down clamp, damage to the O-ring groove or seating surface, etc. At this point, if you're sure you'll be keeping the carb I would go ahead and renew the entire float valve & O-ring, checking carefully for other the problems mentioned above while it's out of the carb. Once the new valve is determined to be leak-free and working well, then go ahead and set the float height.
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this bike lives @ 5000-6000ft
The stock jetting will be rich for sure, then.
Ray