My Jazz is the same model as yours Chris, I have no complaints about the road holding, certainly it is no sports car but it wasn't designed as one. Tyre pressures are important but that applies to any car. I do not believe that being a CVT is relevant, I have owned both manual and CVT versions of the same model and did not notice any difference in the handling. I suggest that you have another check on the tyre pressures. I had a pressure gauge that slowly developed a fault that meant that I was gradually inflating them to higher and higher pressures, this certainly affected the handling in that it made the car more 'twitchy', the fault was spotted when the car was serviced. Reducing them to the correct pressures, the manufacturers spec, solved the problem.
Vic.