White smoke out the pipe is not a good sign. And also the amount of gooey spills is more than normal. Are you sure the engine oil is still fine? If water was coming in to your lubrication system in any significant amount, the oil would get creamy, all of it. Pumps do a fine job mixing... How does it look on the stick?
And are you absolutely sure it is not overfilled? How much oil do did you fill on last change? Do you drain both tank and engine? (Not that I question your mechanic skills, it just that some people just don't read their manuals
)
Is there any risk that you migth have gotten water into your vent hose when washing? My thinking is that there might be a combination of problems: 1: Overfilled on oil makes it splash up into the breather, and water inserted into hose makes it gooey.
2. The hard starting might very well come from a blown head gasket. If ever so little water makes it into the cylinder, starting would become very difficult.
However, the white puffs of smoke on restart is by itself a call for disassembly.(unless you are riding in very wet conditions with lots of water crossings. How is your air filter? Soaking in water?)