It definitely sounds like you need to go through the carbs. I do not put much stock in running any kind of cleaner through the carbs. I have just never seen any of it work. I know it is inexpensive to try and easy to use but I have never seen it produce any positive results.
I would take a good close look at your low speed jets and check your low speed screw settings.
Exactly what are you doing that produces this "heavy drag"?
Thanks
RSRBOB

Thank you for the additional information.
I think I understand what you are feeling now but do need one further clarification. Is it sluggish, in a way that sounds like it is blubbering or gurgling as you try to take off? Is it worse after you have been idling for more than 30 seconds? If you were to come off of full throttle, let the boat settle in the water back to idle then immediately hit it again, would it respond quickly or is it still doggy?
Yamaha's are traditionally rich down low (low RPMs) and I am wondering if that is what you are fighting. The low speed screws on the carb body towards the base.
Here is a diagram of your carb set up. The low speed screws are reference #33.

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I never did ask you exactly which model 800cc Wave Runner you have. They put that engine in both 2 seater boats and 3 seater boats. Also what year is your wave runner?
One thing to understand as well, it is common that the engine will loose more rpm's in a hard turn in one direction compared to the same hard turn in the other direction. The easiest way to explain why that happens is think of the jet pump as a saw blade. When you are sawing downhill, like with the direction of blade rotation, there is very little resistance to moving forward. When you are sawing against the direction of rotation, there is a tremendous increase in resistance to moving forward. Your jet pump is being loaded by the water coming into it, in one direction it is uphill and the other direction it is down hill, so to speak. This additional pump loading is enough to cause the RPM's to drop more in one direction than the other.
Thanks
RSRBOB