My stand up was doing the same thing ran like a stripped ass ape on the trailer then would put it in the water and you would only be able to putt around on it and then it would die. So try taking off the carbs and check the reeds!!!! I'm not sure if that ski is a triple carb but usaually a reed will be broke/shattered and thats why you could be having that problem also try changing the spark plugs. Hope this helps!!!!
I had the same exact problem. What I did was siphon off some of the gas from the bottom of the tank to get whatever might be down there that was blocking up my tubes. Took the fuel lines off and cleaned them (mine had a lot of gunk in them). Changed the fuel filter and also I took my ski off of the trailer, tipped it on it's side and ran it, incase I had water in the carb bowl that would allow the water to get out of there(I had recently flipped mine and had gotten a gallon of water in the engine). I think that what your talking about is that the engine is not getting enough fuel. Clean all filters and tubes. I also ran some concentrated carb injector cleaner through the engine. I took it out the next day and it ran fine.
Tune up consist of plugs and good gas on that particular ski! you said it idles fine on the trailer, does it power up on the trailer? if so its posssibly an impeller prob. but not likely! I really need more info! Possible fuel delivery problem, water seperator. you need to start with the basics, If you need those steps you cam Pm me and I will tell you the proper steps to diag. your prob. good luck!
I had a similar issue with my js440, what i found was my expansion chamber was loose, it ran great out of the water but had no balls under load, I just tightend up my exhaust and away she went. let me know when you find the issue I just bought a 97' 900zxi so I'm trying to gather as much info as possible. just in case.
good luck man