The opening the throttle and running wide can be dial almost completely by setting the suspension properly, usually happens because the rear squats and the forks return too quick changing the geometry and the bike goes wide.
Shutting the throttle loads the front but can unsettle the bike which is why a balanced throttle in the correct gear is less unsettling.
The 600 in standard guise was no way near as bad as the 1000 in standard guise for for running wide out of the bends if you power on the throttle
I presently run a Hagon rear shock with an uprated spring (Standard Hagon Spring was too soft) and Hypro progressive front springs with 15w oil. (I use progressive instead of linear because I do a lot of two up touring) The 15W oil in the 600 slows the rebound preventing the sudden unloading of the front and keeping it in line.
Took me quite a while to get it sorted on the 1000 because I was running standard front forks.
Considered changing the front end but when I finally got it working I kept the standard front end.
I have a S1000RR rear and Wilber progressive front again and 10W oil (Progressive because I tour two up on it also).
As some Foccers have stated previously the Hero Blobs at the end of the footrest are your guide.
Thankfully they fold and not dig in like the bikes I started riding back in the 70s. Scary foccing things, solid footrests, no damping and ABS brakes (Anything But Stop)
Mostly it is about confidence in dropping the bike and believing it wont slide, but this also means reading the road conditions correctly.Being in the correct gear for the bend is also important and riding on the throttle through it this prevents the suspension loading on the brakes and unloading off the brakes and accelerating.Trail braking is useful but not really necessary if you are in the right gear for the bend.
Good practice for using the gear box is to use a good road with fast and slow bends you are familiar with and try riding it without using the brakes, just the gears for slowing down and balance the throttle riding through them. You will find at the start dropping to low in the gears but it is all practice. It forces you to read the road and the vanishing point better. You will find you riding becoming smoother and quicker as your reading of the road improves.
Most of us have a limit as to how far we feel safe to bank over and when we go in too quick we have a margin of error to allow us to bank over. unfortunately the inexperienced focus on the point they don't want to hit grab a handful of brake and go straight on to it. The experienced will trail brake gently bank over further and look at where we want to go.
One of the most difficult things to over come on track days is this margin of error, mostly because it take us out of our comfort zone.
The counters steering is definitely instinctive, but you can push it further than the instinctive amount, attached pic has Jason O Halloran counter steering