totally have a stuck float valve, or stuck float. Not a tough fix. Floats push spring loaded needle valve, to open or shut. My bet would be needle valve is stuck to the valve seat or seal. I had opposite problem on 660. Got sand in it from dunes, valve stuck open. Puddle of gas on the trailer, relatively easy fix though.
Once, I had a honda 400 motorcycle with leaking bowl problem..new floats, floats I got were too big and would get stuck open when bowl was full, so it would run great for 5 minutes, then flood, then gas would start pouring out of the bowls. Your floats may be stuck down.