Worse case, a new carb is under $20 if all else fails in the cleaning and adjusting. I just bought this one for a 6hp that I was working on where the carb had seen much better days...I did not even have to adjust the idle or main jet it ran great out of the box but I was probably just lucky.
New Carburetor for Tecumseh Troy Bilt Horse Tillers 5HP 6hp H50 H60 HH60 Carb | eBay
New Carburetor for Tecumseh Troy Bilt Horse Tillers 5HP 6hp H50 H60 HH60 Carb | eBay