Hi Jim. I'm not sure what Abarth used to do. Lowering the car will help for sure. You can add a restraint to prevent the trailing arm fro dropping too low by using a short piece of stainless steel wire with an eyelet at each end and attached to the body and trailing arm. You could use a camber compensator, but I am not sure where you can find them now. Adding a sway bar will help. See Scuderia Topolino's website for info on this. I adapted 850 swaybars to fit on a 600 once, and it worked well. You can buy Abarth replica ones. (I have a set of these for my 850TC replica project.) Also, stiffer shocks will help. You can get Koni shocks, or just take the stock Fiat ones apart and use heavier motorcycle fork oil. I would expect that wider tires and wheels will help too.
15-20 years ago, I built an Abarth replica. I cut the rear springs (and re-arched the front ones), used the 850 swaybars, and installed heavier oil in the shocks. I raced the car in autocrosses and flung it around corners on the street. I never had any problems or worries about the trailing arms tucking under.
What I am more concerned about now is, replacing the stock stub axles so one doesn't break in hard cornering! I am gong to install CV joints and stub axles from Scuderia Topolino. BTW, I destroyed quite a few of the rubber-filled couplings from doing to many "jack-rabbit" starts on the street. I'm hoping the CV joints will help prevent this.
Gil