Testa1856,
I have a FA 120 that has a carb that looks exactly like you pictured. It is not mounted on anything so I could look it over closely. It's barrel does not close entirely either and I believe it would continue to run with the amount of opening that remains. The "retainer" screw is installed completely snug against it's head. I backed it out and it allows the barrel to close fully. I believe like you suggested a small washer under the head of the screw would allow the amount of adjustment that you need to kill the engine.
Regards Don