Make sure to rebuild and/or replace your carburetors. It's very important the fuel system is in tip-top condition or else the same problem will occur again in a short time. By this I mean the engine should run correctly, no lean hesitation, bogging or poor performance. If you experience poor performance then stop using the engine immediately until you can locate the problem, don't "finish the day on the water" unless it's being pulled by another boat or paddling!
There are some very small precision drilled passages in the carburetors called the pilot ports, these tend to corrode inside and the passages diameter is reduced. This causes a lean fuel mixture, usually lean hesitation and stalling, engine falls flat on it's face during acceleration, especially light acceleration.
In short, disassemble and clean those Mikuni carburetors thoroughly internally, even then you may still experience piston-eating hesitation.
There are many versions of these carburetors, there should be no need to change the calibration so just plan for some new parts such as gasket kit, including needle valve and seat. Probably a new diaphragm would be a good idea especially if original one is not soft like a rose petal.
KEEP THE ORIGINAL metering spring (if it's original, hard to know for sure), there are at least four Mikuni springs that are different and it's easy to get the wrong spring and that doesn't work well.
You might want this manual, it helps to explain about how the carburetor works and can save you time. This manual is not specifically for your carburetor, it covers several models and is general information. For specific info concerning calibration detail, use the specifications given in the Seadoo factory shop manual for your engine model and configuration.
http://www.mikuni.com/pdf/sbn_manual.pdf