Well if its a dynojet, you'll probably need dynojet mainjets, stock ones won't work as the emulsion tubes are usually changed with the jets. Did you get the unused jets in the kit?(ie, 96, 100) Are you sure it's rich? "Breaking up"(incomplete burn I'm assuming) when hitting hard on the throttle usually means it's starving for fuel. If you hit hard on the throttle and it sort of loses power and sounds kind of wallowy and "wet" then it's usually rich. Lean will sound more "tinny" and a higher pitch. What notch are your needles set to?
A good way to find out is take it on a long highway ride with higher rpms then pull the plugs when cool. It may just need a notch up or down on the needles if they are adjustable. I had my bike do something similar with over half throttle inputs and I just added a shim to the needle(made it richer at mid-range) and it fixed it.
For fun if you want to change the needles so that they are richer or leaner do this
Bad ASCII diagram
__ <----TOP OF NEEDLE
I I
I_I
I_I
__ I_I__ <------------ C-clip (in middle position
I_I
I_I <------ The little dashes are notches cut into the needle where the C-clip sits
I I
I I
I I
I I
I I
I I
I I
I I
I I
V
Move the C-clip down a notch or two to richen up mid-range and larger throttle inputs
Move the C-clip up a notch or two to lean up mid-range and larget throttle inputs.
Take a look at the plugs if the centre white electrode has smudges of dark carbon you're probably too rich in the mid range/wide open throttle inputs. If its bone white, you're probably too lean at larger throttle inputs.
Also look at the base ring, which is the ring around the base of the plug where the ground strap is welded to. If you see dark sooty deposits you're mixture screws are probably a bit rich, if there is no or very light deposits that don't go all the way around the base ring it probably is a little lean you can turn out the mixture screws an 1/8th of a time to richen the low throttle idle mixture or turn in the mixture screws an 1/8 of a turn at a time to lean the mixture screws. Since you already said that it idles very nicely I wouldn't touch them for now since your problem is mostly with the larger throttle inputs I would start with adjusting the needles. Even if the main jets are off a bit adjusting the needle will help considerably.
WARNING: When you take the carb caps off, because you have a G2 Bandit, put a rag in front of the carbs as there is a little O-Ring that can get lost easily. Take the cap off CAREFULLY.
Is there an extra hole cut into the airbox or is it stock? If you want to see quickly without adjusting anything, whether it's rich or lean you could take out the rubber snorkle at the rear of the airbox(you can pop it back in later) which will allow more air to flow into the engine. If you are too rich you should notice an immediate increase in power. The problem with the G2(2001-2005) bandit's airbox is it designed for the 600 so it's constantly starved for air. While the K&N helps a bit it's still restricted by the dinky air intake, no amount of high flow filter can fix that.
For example I bought a hole shot kit in which you install larger jets but also cut an additional 1.5" hole in the lid to double the amount of air going in there. If you install larger jets without adding to requisite amount of airflow you just make it horribly rich, even with a high flow exhaust and filter it's still not enough. Removing the snorkle temporarily will turn the 1.5" hole with a 2" hole thereby increasing the total amount of air going into the airbox. It may not be a permanant solution but at least you'll be able to figure out if you need more air in there.
If I were you, for fun I would remove the snorkle(you may lose some low end torque) since it requires the least amount of work and see if you suddenly get some more power and it starts running better. If the hesitation is worse, then you are too lean at larger throttle inputs.
It may not be a permanent solution but at least you'll know the deal of what's going on. Can you post a pic of one of your spark plugs?