Yep, the hard the spring, the more 'work' that end of the car does, so a harder rear generally means more oversteer.

So, you could put a 120y swaybar on the front perhaps, or stiffen the front a little...

The stock rear geometry has a fair bit of roll understeer, so all things being equal it shouldnt oversteer without being provoked.

Ive found that 1200's love having suspension travel, a higher car will handle more predictably than one which has been lowered without any provision for more travel....