If I am cruising along at say 50 km/h with the throttle at 0 and suddenly snap the throttle on to say 50%+, I notice a definite jerk/lunging motion as the bike begins accelerating. This occurs in any gear, although is more pronounced in the lower gears as they obviously have more "grunt".
The same things occurs the other way, if I am doing say 100 km/h at 6000 RPM with the throttle at anything over about 40%, and I quickly snap off the throttle, the bike again lunges/jerks, almost throwing me forward a little out of my seat.
It makes riding at a fast pace through corners difficult, as even with a gentle throttle roll on at high RPMs/speed, the jerk/lunging motion is uncomfortable at best, and upsets the handling/suspension at worst.
Is what I have described the infamous "herky jerky" throttle? If so, I'll give adjusting the TPS a go and post back results.
No. While this technically is herky-jerky throttle response, it is not caused by some fueling problem, or other problem with your bike, but by herky-jerky throttle input (by you). Let me elaborate: In first gear, a GSX-R 600 makes about 60Hp with wide-open throttle. Say it makes 40Hp at 50% open throttle. When the throttle is closed, engine and drivetrain losses cause you to decelerate, so in a way it makes negative horsepower, so when you "snap the throttle to 50%" you change the power output of the engine by more than 40Hp in an instant. This is going to cause a proportionate change in acceleration from braking to accelerating, upsetting the chassis as you note, and throwing your body backwards.
The situation is similar, only reverse in the case of suddenly snapping the throttle shut. The only remedy for this is not to do it. I don't know what other bikes you've owned, but the only way to get away with jerky throttle input on the scale you describe, is if the bike has a low power-to-weight ratio, computer-controlled throttle smoothing your inputs, or both. You also mention having problems when you smoothly roll the throttle open. This might be, in part at least, due to a "herky-jerky" throttle, but it may also be that your inputs are just not smooth enough. Finessing a throttle that changes power output by 80 or 100Hp from 0° to 90° can be hard, especially when that power is applied to a load of less than 300kg.
The "herky-jerky" is generally associated with the transition from that portion of throttle opening, where you're decelerating, to that portion where you're accelerating. Depending on gear and speed, the point on the throttle's travel where that happens changes, but your throttle input at that point is especially critical (for reasons that have been explained before and you can look up with a site search). It can also be related to the operation of the throttle when ever you open it from completely closed, or close it completely, in which case a properly set TPS is critical.
Finally and please don't take this as an attack on your riding skills, or personal insult, but your comments may be implying that your riding skill doesn't match the machine you're riding. If this is not the case then all is great, but if it is, it can be dangerous to you and those around you, so that you need to think about this as dispassionately as possible. Consider riding more conservatively until you gain some experience on your bike's behavior and response and on the potential dangers it may pose and accelerating your learning process by reading a couple of books on riding technique, attending a couple of riding school session, etc.