Dropping the front will quicken steering and make it drop into corners easier. You can achieve the same by raising the rear ride height, which your bike has an adjuster for and is reasonably easy to do. The downside, as previously mentioned is the possible loss of stability. Its something worth experimenting with though.
As far as going to a lower profile tyre, this does not have the same effect, the lower profile tyre has a flatter / rounder profile it will actually slow the steering and add stability. A higher profile tyre is usually a steeper/sharper profile and will give better side grip as there is more side..
On my zx7 I had the front dropped 7-8mm and the rear raised 10, lost a bit of stabilty but was a good compromise for track / road. The zx9 has the front dropped 5-6mm and the rear raised 12-13mm (max) I'd drop the front a little more but I hit the engine case on the deck..

Dave
2010 Z1000
ex bikes
05 ZX-10R Race Bike - No.77
95 ZXR750R M Race Bike - No. 75
98 ZX9R Race Bike - No. 000
zx6r, zx7r, GPX750, GPX500, lots of KX's.

I ride way too fast to worry about cholesterol