Welcome to the forum.
Lots of good people with good advice here.
At the top of this two stroke section is the carb rebuild thread. It is the best reference for working on the sea-doo carbs.
Fuel problems are one of the biggest issues so, as said by Mikidymac, rebuild the carbs, that fuel selector switch leaking air can throw things off and make sure you don't have the original grey fuel lines that deteriorate and gum things up.
It can't be said enough times. Only use original Mikuni carb kits, needle and seats. Just because the ebay add says muikuni doesn't mean you are getting OEM parts.
Check the jet pump condition by pulling the cone off the pump. Drain the oil, flush with brake clean, refill with oil and watch out for the core o-ring when you put it back in because they like to get pinched and not seal.
Grab the exhaust pipe and try to rock the motor side to side looking fir a broken motor mount.
Check your 4 bolts holding the tuned pipe to the exhaust manifold.
Do not use any extra fuel filters in the machine. There is a filter/ water separator by the steering column and filters built into the carbs. Any extra filter cut into a fuel line just give you another potential air leak to fight with.
