Higher fuel level on one carb doesn't necessarily mean the float valve is "gone" - the float might just need adjusting. Check it against the spec in the manual.
To check if the valve is seating properly, clean it out thoroughly, bring the float up to seated, connect the fuel and see if it's leaking.
If the oil is filling up with fuel that fast then it does seem like there's a problem with the floats or float valves. Now it's back together - did you check the fuel height as I described? If so, where was the fuel level relative to the joint face between the float bowl and carb body?
Generally any breather hoses from the head will go to the top of the airbox, with a crank-case breather going to the bottom of it.
Soooo, if there are hoses connected to the airbox - what have you connected the other ends of them to?
The over-flow breathers from the top of the carbs generally just route down the back of the engine, along with the tank breather hose.
Other than that there should be the fuel hose from the tap to the carbs, and probably a vacuum pipe from the inlet tracts to the petrol tap.
What else have you got left over?
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