I suggest that you do a compression test and if the readings between cylinders vary excessively, then do a leakdown test to determine where the compression is leaking.
As for a carb cleaning, if you are careful while disassembling the carb, you will be able to reuse the gaskets. Don't allow carb cleaner to contact the gaskets as it will destroy them.
My 44P777 had stuck rings on the starter motor side cylinder at which time I chose to replace the engine. Needing better air filtration was the 2nd reason that I repowered.
If you think that Briggs parts are expensive, stay away from Kawasaki!!!
Just a few thoughts from Mad Mackie in CT:laughing::biggrin::smile: