I see this problem alot ie " the pogo effect"
when you are unsure of what your bike is going to do after you drop the clutch or pull back in a power wheelie your first reaction is to lay of the throttle, and by lay off some people close it all the way. very scary.
couple of pointers on how to avoid this.
1. similar to your Katana600, start slowly finding the throttle points where the front tire is coming off the ground 1 to 2 first.
2. after getting comfortable at this angle and speed, start shifting your weight further towards the back of the bike, it should come up another foot or so but you will know exactly how fast you are going and how many rpms you have left in front of you too smooth out that landing.
3. when learning wheelies it helps a bit to take some of the tire pressure out of the rear tire, this will give you a larger patch of tire to work with when you are up on one wheel and also will make the bike feel more solid when up as opposed to worrying about the side to side motion
4. get comfortable with that rear brake it is a great safety net and will help with overall control of yours wheelies.
the key to wheelies is to understand what your bike is going to and never panic, I see idiots on cbr600s all the time ripping up a wheelie and then bouncing it up and down, open to closed throttle, TERRIFYING to me. I have the ambulance on speed dial for people like this.
If you keep your bike at reasonable rpms, which for our torquey bikes it does not have to be that high at all, your not going to flip.
plan out your wheelie in your head, and when you say to yourself, ok i'm going to try and get this wheelie a bit higher, plan to be scared and plan what your going to do when that happens. don't wait for it to happen and do something dumb like pop it up pull in the clutch and slam the back brake....that will hurt.
disclaimer, unless you know what your doing, don't touch the clutch during wheelies, you have a lot more control over your bike when it is in gear
just know a simple shift of your weight and a little bit less throttle will bring you down nice and smooth.
good luck out there.