You have 2 stroke oil in the injection tank right? Rebuild your low pressure pump cheap and wont hurt if it dosnt fix it, I would test fuel in water again I'm not sure if I believe that did you change both water fuel separator filters? Sounds to me like a fuel delivery issue I'm going through the same thing with my ficht motor and if it was water in fuel it would start and die immediately it wouldnt run while pumping bulb, Why your at it change your primer bulb a bad bulb can be the issue and easy fix and your spark plugs make sure there champion OEM plugs there's no cross reference if you see some Ngk that says its cross reference trust me dont use it. Your outboard will be fully tuned up now rebuild your low pressure pump. Then if your still having problems buy a high pressure pump. Whatch this video.
You will be better off than I am I figured this out on my own with out help no one on this forum answers.
Please help me with my outboard i need to fish (: