What I did today:
Pulled the spark plugs. Sprayed WD40 into the cylinders. Put the bike into 5th gear and ran with it up the street until I have puffed out most of the fluid. Replaced sparks plugs and now I'm looking at my carbs. The floats seem fine. I checked the levels and they are in spec. They don't get hung up or anything.
I did notice a fair bit of black gunk on the cylinder head when peering down at it through the spark plug hole with a flashlight. I hope this isn't a bad sign.