Oops... Sorry NOT ABR... Should be ARB (Anti-roll Bars)
The primary function of anti-roll bars is to reduce body roll by adding to the roll resistance of the springs. Anti-roll bars are used to reduce body roll during cornering. Most cars have a front anti-roll bar, and most sports cars are going to have both a front and rear bar.
But your problem is as explained by others caused by so many reasons. But I really doubt you have soft springs as told by your mechanic. If so I think changing form your existing setup to a harder setup will aggravate your situation. You can have a big balloon sizes tyres, softer suspension, standard coils, to somewhat overcome your prob.... but your ride might look like a Honda HRV . You have a great car. Please don’t do any injustice to it.
If you don't mind could you please post a pic of your car.... I just want to see it's the same HP12 that I'm thinking of that you have.