WET PLUGS
what brand plugs did you use? i happen to be quite certain plug brands offer different available heat ranges, and whatever the OEM or this forum recommends would be better to put in the ski so the cylinder temperature at the spark plug is just right. trust me, you dont wanna mess with heat ranges or know what they are or know exactly which one to put in and why. (i know this is VERY important in cars, not sure about the skis though)
many thinks can cause a computer controlled engine to run rich, so many sensors to check its kinda ridiculous. i would start with OEM spark plugs and maybe some fuel system cleaner (stuck injectors will make for wet plugs.) i would also get a spark tester and check for a nice, crisp blue spark.
FOR THE BATTERY ISSUES....
try replacig the battery. if it has a typical lead-acid battery in it, replace it with a glass-mat battery. i have about 4 seasons on my current battery, i got one season out of the typical wet-cell battery. hope this helps