There are three Avionics owned by members of my club. They all have the torsion type axle and tow quite nicely. Mine (a 2004) was not quite as good as the other ones though until I put 175 size tires on it in place on the 165's it came with. The newer ones came with 175's from the factory.

Shocks certainly wouldn't hurt but the suggestions about increasing the tongue weight are worth following. It may make a significant improvement and would be easy and inexpensive to try.

Trailer stability is weird though. The Pfeister trailer my club has for a Twin Astir has almost no tongue weight when loaded but towed nicely behind my old Nissan pickup. Once, when taking it through the Rockies it had been loaded the "proper" way by the club expert - he put ballast right up front so it had about 100 pounds tongue weight. Loaded like that it tried to throw me off the road at anything above 75 KMH towed by the same truck. Go figure.