Putting better suspension in seemed to make a big difference to my 111r, using sport soft tyres atm and it sticks pretty well to the road. I've gone a bit beyond these mods too with maybe 5-10k more spent on upgrades. It becomes an awesomely fun car.
I dont find it that hard to steer.... steering seems to work quite well in fact. now getting it to go where i want it to go...... thats another storey!