You should see at least 12.5 volts at the battery before anticipating it will start, if voltage at the battery drops under about 11V while cranking there's a good chance there isn't enough voltage to operate the CDI ignition. Remember, even if there's enough high voltage to jump the spark gap in open air, this might not happen during the compression stroke, it's more difficult since plug voltage must be higher across the gap during the compression. Usually in this case though, the problem is the plug itself (ie: the voltage rises enough to either jump the gap or bleeds down the side of a contaminated ceramic center electrode insulator).
Since the first 30 minutes of the water testing went well, I'd say the carburetor calibrations were correct and you should go back to where those were. Also, this means the cooling was adequate.
I don't recall if this ski has the DESS system or the older simple lanyard switch but the older simple lanyard switches were notorious for poor connection in the switch and often were found to be the cause of ignition issues.
One way to eliminate the possibility of no or lack of fuel flow is to run a hose from a small fuel tank like drop a hose into a gallon can of pre-mix and see if this makes a difference. You have to be certain the fuel pump can pump fuel and also that it's not sucking air.
If you're unsure of the oiling system, you could run pre-mix in the fuel tank to temporarily supplement the oil supply, a dry carb though doesn't pass fuel thus won't pass oil as well, in this case. commonly we see plenty of roasted 2-stroke motors due to one carb is dry and thus one cylinder isn't receiving it's oil and fuel through that carb so take precaution and heed the notion of carbs not fueling correctly b/c this always leads to engine damage in all cases for 2-strokes. Too much fuel where the plugs tend to foul is safer than lack of fuel.
I tweak my 2-stroke carbs till they're on the clearly on the rich side of the rich/lean conundrum then go back toward lean gradually till the plugs run a normal color and normal power is produced. That is, it's much better to be slightly on the rich side of the knee point. A 2-stroke will literally put out it's peak power and run like stink with gobs of power as mixture reaches that knee point, then over the cliff of seizure shortly afterward due to not enough fuel. Go richer till you hear that 4-stroking rich burble then back toward lean till it cleans up. These carbs cannot be tuned out of water aside from correcting gross problems, they don't make power on the trailer and the plugs will run stone cold.
One more thing to investigate is the condition of battery cables b/c salt gets under the insulation and corrodes them into pencil-lead thickness. So if battery voltage remains over 11V while cranking there could be enough loss through the cables to allow CDI module voltage to drop under about 10V, which is approaching the lower operation limit.
Keep plugging away, you'll find it!
