I suspect you "still" have a gummed up carb. Just how did you clean it, and with what?
I've had great luck with spray carb cleaner, but remember there are many tiny passages that can get plugged by bad gas. Gas today has ethanol and other additives that do not store well. Using a stabilizer does a good job of extending storage life beyond a month or so. This is very important for seasonal engines that sit for months.
First, try a double dose of Sta-Bil, or Seafoam in fresh
gas. Go through your starting procedure several (many?) times and see if things clear up. You can even try keeping it running for a while by continued priming.
My second step would be to pull the idle/speed mixture screw and spray cleaner liberally well into the hole. Be sure to count the turns gently into the seat before removal.
Use that count to replace the needle for a good starting place.
Here's the Briggs site
Type in your model number for info.
From the site:
Adjusting The Idle Speed And Mixture
On some float-type carburetors, you can adjust the air-fuel mixture and engine speed at idle. Check for an idle speed screw designed to keep the throttle plate from closing completely, and an idle mixture screw that limits the flow of fuel at idle. If your carburetor contains these screws, proceed below.
With the engine off, remove the air filter and air cartridge.
Locate the idle mixture screw and turn it clockwise until the needle lightly touches the seat. Then, turn the screw counterclockwise 1-1/2 turns.
If your carburetor has a main jet adjustment screw at the base of the float bowl, turn the screw clockwise until you feel it just touch the seat inside the emulsion tube. Then, turn the screw counterclockwise 1 to 1-1/2 turns. Replace the air cleaner assembly and start the engine for final carburetor adjustments.
Run the engine for five minutes at half throttle to bring it to its operating temperature. Then, turn the idle mixture screw slowly clockwise until the engine begins to slow. Turn the screw in the opposite direction until the engine again begins to slow (image A). Finally, turn the screw back to the midpoint.
Using a tachometer to gauge engine speed (image B), set the idle speed screw to bring the engine to 1750 RPM for aluminum-cylinder engine or 1200 RPM for engine with a cast-iron cylinder sleeve.
With the engine running at idle (image D), hold the throttle lever against the idle speed screw to bring the engine speed to "true idle." Then, repeat the idle mixture screw adjustments from Step 4 to fine-tune the mixture (image C).
Adjusting The High Speed Mixture
Some older carburetors contain a high speed mixture screw, near the throttle plate and opposite the idle speed screw. Under load, the high speed circuit increases air flow through the throat. Setting the high speed mixture involves running the engine until it is warm, stopping it to adjust the high speed mixture and then restarting for final adjustments.
The screw may have a plastic cap that needs a proprietary tool to adjust, but you could use a Dremel to cut a slot for a screwdriver.