I was recently gifted a Craftsman YS4500 with a 20HP Briggs single cylinder. It had been sitting in a neighbor’s garage for at least 5 years, probably longer, because “it was blowing smoke out of the muffler.” It turned out to be a blown head gasket. Looking at the consumer comments of those who bought head gaskets for Intek engines, I learned that these big Briggs Inteks go through head gaskets like the Gabor sisters went through husbands. In my research I also read that a bad head gasket could cause surging. I notice that you have replaced everything else. So, maybe do a leak down test and eliminate the head gasket as the cause. Or, just replace it. Intek head gaskets are really cheap and easy to replace and if your engine is typical, you’ll need to replace it in a year or two anyway. Good luck.
