If I'm not mistaken, I believe this is the same engine that is used in my Yamaha Super Jet (701cc). Mine has been a really good engine, no issues.
The issue of running fine out of water, but bogging in the water, sounds VERY familiar, I had the same issue with my Tigershark 1000. With my TS engine, I came to find out that the CDI box was mounted too far back, causing the rear plug wire to intermittently connect. Out of the water with no load on the prop, it would rev normally. But in the water, it didn't want to rev up, and when I could get it to run, it had a horrible sputter (running on 2 of 3 cylinders will tend to do that!)
So, do the simple thing first, and check your plugs, and your wires, make sure you are in fact getting fire to both plugs. Also, look into the throat of the carb when you hit the throttle, see if you can detect fuel spray. While you're at it, the next thing you want to check is the fuel filter, make sure it's not clogged. Very simple things can cause hours of headache, searching for the problem.
Next, check to see that the impulse line has not disconnected from your fuel pump. The up-and-down stroke of the pistons causes positive and negative pressure, which is pulsed through a hose to the fuel pump, and it operates the diaphragms, causing it to pump fuel. If this line comes loose, or has a leak, the fuel pump will not pump properly.
Also, remember that 2 stroke PWC engines are not like the fuel system of an outboard. Where an outboard gas tank has a vent that allows built-up pressure to escape, the PWC does not, and it is this internal pressure, along with gravity, and the fuel pump, all working together, to deliver fuel to the engine. So, if you have an open vent line, you need to install a check valve in that vent line, so that it can pull air in, but not let it out.
Once you eliminate these variables, if it's still not running right, then it's time to look at the carbs. First, get the factory specs for the carb settings, and set them to that, and then experiment by adjusting 1/8 turn to either side of that setting, to see if there's any change.
DANGER! BE VERY CAREFUL WHEN TRYING TO DIAL IN CARBS. IF YOU HEAR ANY PINGING SOUND FROM THE ENGINE AT WOT, LIKE THE SOUND OF MARBLES RATTLING AROUND, IMMEDIATELY REDUCE THROTTLE, THAT SOUND IS DETONATION, AND IF ALLOWED TO CONTINUE, IT WILL DAMAGE A PISTON, POSSIBLY BURNING A HOLE RIGHT THROUGH THE TOP OF IT.
If an adjustment doesn't change it, then the next step is to disassemble and clean the carbs, being sure to check the internal filter, as well as the diaphragms. Also, look closely at the jets to make sure they're not clogged or obstructed.
One of these procedures will correct the problem, it's just a matter of figuring out which one. So, start simple, making sure you have fire and fuel at each cylinder, and go from there.