Just a hint from my experience with Honda and Honda clone gen carbs and your symptoms.
On my Honda type carbs before storage I shut off the fuel supply and let the engine run until it dies, then remove the little MM bolt in the side of the carb bowl and finish draining the gas, then leave the drain bolt out and pull off the fuel line going to the carb and send it auto xmission fluid in the fuel line until it runs out the drain hole.
Before starting the unit next time I pull the drain bolt turn fuel supply one until fuel runs out re-install the drain bolt and go.
It will smoke for just a little while then clear up.That little drain bolt will not drain all the fuel out and when the engine quits running with the petcock off a little bit of fuel remains in the bottom of the bowl and especially if it's ethanol it will get a muck gel.
You probably got to it before it got to the point of removing the bowl for a cleaning. and some of those bowls will rust and they have too be replaced, not just cleaned because the little rust particles just keep on growing and coming back after each cleaning. Go ahead and get yourself some of the bowl gaskets because you will eventually need them. sometimes you can remove the bowl clean it and use low pressure air, like 15 pounds around the lower jet area and it will re-store all ok, especially in an emergency when the gen is really needed.
I converted some of the emergency gen's to (tri fuel kits) using propane using US carb kits and it dowes not clog the carbs during storage. This is on gen's that are really needed in a emergency and long term stored.
The real enemy of gens, especially gasoline type is not running them at least once a month.