Sounds like needles and seats to me, once warm the worn out needles and seats flood the engine with too much gas. If it starts on land but not in the water when cold then the battery voltage drops below 10.5 volts when starting in the water due to the extra load from the water, and it will not fire. Just figured this out myself this year. One of my best running and reliable skis started on my dock, I dropped it in the water and it would not start. Charged the battery and it started in the water. A few years ago I had one that started great and then once it was warmed up and running it would not start again and it was worn needles a seats in the carb.