The problem still seems to me to be in the carburetor. The hunting is caused because not enough fuel was getting to the engine. Another possibility is that the spark may have stopped and you may need to replace the ignition.
If you did not use a complete carburetor repair kit, you need to completely clean a rebuild the carburetor.
Here is my comprehensive carburetor and fuel answer that may give you some ideas.
As engines sit or get older, fuel that is left in the carburetor can turn to gum and varnish and cause this and other problems. Also, any gasoline that was left in a gas can for a period of more than 30 days must be discarded because it also has begun to turn to varnish.
Today's gasoline's contain MTBE and alcohol. (Ethanol) They turn to "Junk and garbage" very quickly. Alcohol is partially water (H2O). And they call it "Oxygenated fuels! It is the oxygen that breaks down the organic compounds in the fuel and turns the gas to "Garbage" (Gum and varnish) The fuels we had just a few years ago had no alcohol in it and would store for longer periods of time before going stale... and fuel stabilizers do almost nothing to prevent the fuel from going bad with the changes in today's fuels.
Do not buy gas from the "Discount" Stations. The discount stations get a reduced price on gas because they may be buying fuel that is nearly 30 days old already. You may be getting fuel that's nearly stale right from the pump when buying from a discount station. Purchase your fuel from the well-known stations such as Shell, BP, Sonoco, Phillips 66 etc.
More than 70% of all of our repairs in our lawn mower business are due to this same issue. You most likely have dirt, gum, varnish...etc in your carburetor plugging up the small passageways and jets in the carburetor.
The carburetor must be removed from the engine. Clean all parts with carburetor cleaner and blow out all the small holes and passageways with compressed air. Remove all of the non-metallic parts since the carburetor cleaner will cause them to be disfigured decompose and plug the carburetor as time goes on.
Wash the carburetor cleaner off of the metal parts by washing them in warm, soapy water then rinsing with clean water. Dry them by blowing it off with compressed air. Make sure that all the passageways are blown dry before reassembling.
Reassemble using a NEW carburetor rebuild kit.
DO NOT TRY TO REASSEMBLE WITHOUT USING A COMPLTE CARBURETOR KIT! You will just end up having to do the job again.
ALWAYS clean the fuel tank and replace the fuel line when doing this repair or you may have to do it all over again. The inside of the fuel line disintegrates over time and these small pieces of rubber will plug up the carburetor too. Dirt and water from a dirty fuel tank will also plug up the carburetor. Find the Model, type and serial or code numbers off of the engine and take them to your local dealer to get the carburetor repair kit.
If you do the work yourself, take pictures or at least make a drawing of where all the linkages, gaskets, and component parts go. Correct reassembly is critical.
If the carburetor still doesn't work correctly, you may have to take it to someone who has an "Ultra-sonic" cleaning machine. This machine uses carb cleaner and ultrasonic vibrations to get the very small passageways clean when traditional methods fail.
If you don't feel comfortable with this kind of repair I would suggest sending it to a reputable shop.
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