Hi and thank you for your question.
I am really trying to understand what you are up against here and what is confusing me is the whole description about an OEM fuel line, a fuel rail and the 6 seconds running, I know I am not getting it because it sounds like disconnecting a fuel line makes it run. It is a carbureted ski so it doesn't have a fuel rail, although I do know what you mean about the fuel supply for the carbs.
I am wondering if you ever pulled the spark plugs out when it wouldn't start, before you ever did anything with the fuel line, to see if they were wet, dry or dripping. If not, it would be a valuable piece of diagnostic information.
When you say you removed the OEM fuel line from the outlet of the filter, I assume you mean you disconnected it from the carbs and had fuel coming out the hose at that point. Meaning you believe that fuel is getting to the carbs. But, then you say, when removing it, is when it starts and runs. To be clear, the way you can get your ski to start is to take the fuel line off and crank it with no fuel supply to the carbs?
Let me know if that is the case. If not, make another run at explaining it and we will get to the bottom of this.