I missed the statement that the problem exists with all 3 burners. Therefore it must be something common to all burners, which includes the solenoid switch, the regulator and the common ground for the thermocouples (you have eliminated the tank).
Are you saying you just have to keep re-lighting the burner and eventually it stays lit? Have you tried holding the burner knob in for a extended period (> 30 secs) and still does not stay lit? Once you get a burner to stay lit, does it stay lit until you shut it off? Once you get one burner to stay lit, do the two other burners light and stay lit? Was this boat originally set up for European gas (Butane)?
I guess it is possible if the regulator is not reducing the pressure sufficiently the rushing of gas through the burner could keep the thermocouple from heating
I would definitely contact ENO for advice.