Do you still have the SOS on your carbs? If your fuel line runs straight into your carbs then it's been removed. If your fuel line runs into a mess of tubes then that mess of tubes is the SOS.
If you still have it then fuel won't reach your carbs when the bike is off, so that is why the issue doesn't happen when the bike isn't running.
You likely have a stuck float valve. Did you polish the float seat until it was shiny? Verify that it was shutting off well?
A cracked overflow tube, or broken float (that fuel has leaked into) would cause the same issue.
1981 CB750K with 900 cams
90K KM's, rebuilt head, rebuilt carbs, upgraded valve stem seals
My wife's recipe website that I'm trying to help promote:
Strawberries for supper. Yes, I am a lucky man.