Anyone else does not love the stock BATTLAX HYPERSPORT S22? While I enjoy their grip and stability, I've noticed they make the bike turn heavy. I know the bike is a piggy, but these tires feel "slow" to me if you know what I mean, and I always fill them up to the proper pressure.
I feel safe assuming that there are tires that give a little more "on rails" feeling and lower turn-in latency without compromising grip and wearability. I'd like the bike to lean into the corners a bit easier. The bike feels very nimble while maneuvering lightly, but I feel the tires holding things back when I get a bit more aggressive. I have to push her a fraction of a second earlier to combat the latency, and I really feel the tires fighting while the bike itself wants to lean with me.
I feel like some lean speed has been left on the table to be had. I'm not a knee-dragger at all, but I'd really like more sprightliness, because that would really satisfy me fully. I'm still a 'Busa noob, so I'd appreciate any recommendations for a nimbler road tire that has at least the grip of the OEM ones if there are any.
I found the Battlax tyre to be a little on the slippery side and pretty average on traction tbh. No heavy turning issues here.
Heavy turning as noticeable as you mention (in my case) was only from wearing a flat spot in the centre of the tyre from a lot of straight line highway riding wear. That will definitely do it.
Do a burn out and round it off again.
Low tyre pressure is another symptom... but yours is at 42 psi.
I can't speak for all brand of tyres, but fitment of the correct tyre dimensions and pressure shouldn't make your turning feel that heavy.
As a casual rider and not a track rider, it really doesn't matter too much what brand rubber and tread you use so long as it's appropriate for the bike, riding style, road surface and weather.. but the more you pay, generally the higher performance tyre you will get.
In conclusion, I've never encountered heavy steering from a new tyre; quite the opposite actually.
It's always a cause of tyre wear, lack of maintenance, too large tyre size fitted, low pressure, suspension setup, swing arm length or a seizing steering damper.
I'm sure more experienced members here can correct where I'm wrong.
www.hayabusa.org
Didn't know they had those for the 'Busa. The price is good. You probably saved me a new set of tires if I end up liking them! 
