anton:
that doesn't sound right at all, even with all stock parts.
Instead of changing all the parts, I would try get the tyre+insert correct (that should be 50% of total setup-i believe) and the suspension system (spring + shock oil wt).
Depending what kind of track you're running at of course.
A normal stock R3 should be super stable, off power cornering is moderate, on power will be understeer. At least that is what i experienced.