Briggs & Stratton Excess Fuel/Oil and Choking Out

Perhaps indeed you've blown a head gasket, but I don't see how that would exhibit the symptoms you describe.
 
If we're really talking about the breather tube, one end goes to the carburetor (or intake manifold) and the other to the crankcase. If you've disconnected the carburetor end and stuff is coming out, it must be coming from the crankcase. The only stuff in the crankcase is oil and piston blow-by. The blow-by creates pressure which is relieved  through a one-way valve to the breather tube. I can't imagine that the blow-by is so dense in fuel that it actually looks like dirty fuel. That would mean that a huge amount of fuel in the piston is not being burned and seeping past the rings. First, I'd have to ask how so much fuel would get into the piston. OK, maybe the carburetor is dumping fuel in, not atomizing it. But then, second, I'd have to ask how is it possible that the rings are so bad that fuel pours past them, yet the engine is able to run.
 
Tests I suggest:
 
If you remove the carburetor entirely and shoot starter fluid into the intake, the engine starts, right? If you continue to quirt a little fluid in past the initial start-up shot, can you keep the engine running? And while you're doing that, is a sizeable amount of stuff still coming out the breather tube? Does it seem like more coming out than you're shooting in?
 
If you remove the carburetor, disconnect the spark plug, and crank the engine, does stuff still come out of the breather tube?