Pierre, when you begin the air purge on the ground do this procedure. Run the engine at high idle for approximately 2 minutes then go full throttle then turn the airplane 90 degrees left wing down and run the engine at full throttle for 20 seconds. Then return the airplane to normal level orientation and return throttle to idle. The carburetor metering room is now purged of air, and you can launch the airplane for a cough free flight. You don't have to do the air purge before every flight, it only needs to be done one time before the first flight of the day unless you are stopping the engine after flying by fully closing the throttle to cut off the fuel supply. If you're always stopping the engine after flying by fully closing the throttle then the air purge has to be done again before each flight. Stop the engine by turning the ignition switch to off, then you will not have to do the air purge before the next flight or subsequent flights.
I believe it's your current technique in doing the air purge, not a fault with the carburetor.
Just for your info there is a carburetor gasket/diaphragm repair kit available through any small engine repair shop for the Walbro type of carburetor used on the Saito FG30, FG36, FG40, FG57T, FG84R3, FG90R3. It's Walbro carburetor repair kit #
K10-WYD. https://www.worthpoint.com/worthoped...k10-1786275719
Roger