I will agree that you have a fuel problem from what you are describing.
Have you fully dissasembled the carburettor and cleaned it out thoroughly ?
The twin barrel Nikki is a bi finicky and prone to blocking jets
You will fine plenty of You tube videos if you search "Nikki twin barrel Briggs carburettor "
There is a good photo description of how to clean them on the
Outdoor Power Equipment site
I do not know why but crub tends to build up under the top plate and block the holes .
Also worth checking is the fuel shut off solenoid.
From memory it is 5/16 UNF but take the bowl to your friendly nut & bolt supplier and get a short bolt and alloy washer or a threaded blanking plug to fit in the hole.
Fit that and see if the problem goes away as that is the easiest thing then if it does no better strip down the carb.
There are a few variations of these carbs and be very careful not to mix up the jets, they look the same but are different sizes and it will run like a drunken billy goat if you mix them up as one cylinder will be lean & the other rich.