The problem you are having sounds like an accelerator pump issue. When you first attempt to give it gas, there is a little pump on the backside of the PTO carb that has a plunger in it. When you depress the throttle, it squirts a shot of gas into both cylinders to build your initial vacuum to get the REVs up, then the motors manifold pressure will take over and draw gas from your carbs.
Problem? Your GSX is not suppose to have the accelerator pump. But, since you said you just bought a new pair of carbs, I would check to see if you do have it. How can you tell? With the air box off, look at the front of the carbs and you would see a small (about 1/8" ID) fuel line, like a weedeater, that follows the path under the carbs and into the side of them. On the PTO carb, you will see a small diaphragm plunger, about 2" in diameter.
If you don't have the accelerator pump, then you may have a problem with your low speed jet not being set out right, or you could have the wrong size jets.
You posted this thread in the meet and greet section of the forum, I will be moving it to the PWC 2 stroke troubleshooting.