There will be a number there.

Look on the upwards facing surface just above the nuts that hold the carb to the reed valve/intake. Maybe shine a torch or something there and give the surfaces a wipe clean. 

There are two different types of needle jets in Mikuni carbs .
The type in yours does not have an air jet in that passage , so you're fine there .
In your list of carb parts , you didn't list the needle number , and clip position ( counting from the top ) .

I broke down and ordered Keyster KY-0127 tonight. I was surprised to find the kit DOES NOT include the specialty oring... go figure.
I will find and post the needle jet (and manifold casting) numbers when the kit arrives.

I do not believe the previous owner has been into the carb since he and his pops rebuilt the top end at least 5+ years ago.

I use the Keyster kits too. However they use generic brass with no numbers, or no numbers that correspond to any parts in tuning manuals.  I've been rebuilding with all Mikuni brass. Summit Racing online has everything as does JetsRus (spelling?) The manual will tell what ones are stock.

Is it just totally flooded up. In that case it'll start "without a carb on at all". Just be ready & have a way to stop it or strangle the inlet. Motor would run on choke only at idle & up a 1000 even if every other jet was blocked solid.--if i'm on the right page, bit behind on the story.

Float level you posted doesn't sound right. 

P.S.  "Torch" means "flashlight" in some parts of the world.  Don't get burned by inspecting the carb with an open flame! 

If it's not flooded, from all the crud you found in the petcock almost certainly the pilot jet is plugged up even if it was clean at one point. 

You could solder the main jet closed and it would still start fine. 

Lean or Rich?
I don't think it's flooded I think it's starved for fuel somehow.

Float Level
The float level was my initial thought so I measured the tang height. Then I filled the bowl with fuel. The reason it looks cockeyed in that photo is because I was holding it with my left hand and taking a pic with my right. The floats look lop sided because they were (it is very hard to hold a float bowl in the air and keep the floats even with one another as they bob around in the fuel).

Pilot Jet
I thought the same thing re: the pilot jet. The pilot jet was cleared with carb cleaner and compressed air, I can see through its main bore and each of the 4 holes on the sides.
I also sprayed the passageway and held my finger inside the carb to make sure I could feel air passing through the different passageways.



 

Here is a carb jet chart from a parts fiche for anyone else that might be reading this thread in the future. I attempted to translate it into a table
 
 

 

Well now... mines got issues now... So I'll glean some of yer info.. Thank you! 
Sneezles61