it's the tires most likely. IIRC, the shinko 804/805 and 705 are Bias ply, and so don't have quite the same characteristics as a good street radial. I just put a set of 705s on my 2015 1000 (had them on 2 other 650's in prior years), and i noticed that the handling is similar in that theres lots of fall in initially, and theres the usual odd transition from low speed to high speed where you turn handlebars in the same direction to turn then switch to counter steer to maintain.
What i noticed that IS different is that the front steering is very sensitive to rapid input, and will shake more, as if it's low traction in the front. on the 650's the tires liked being near or even slightly over the recommended max pressure on the road, so i dropped the front pressures by 4 psi (didn't help much). but i then increased rear preload by about 3 mm and it helped quite a bit by putting more weight on the front tire. so i would recommend playing w/ tire pressures a bit and preload and see if it helps.