The racing transmission is pretty much a requirement with the Vitz. Crank the "auto setting" down pretty short, like in the mid 20s, and give it a try. Without it, even a powerful Vitz feels like it's on Quaaludes. I guarantee it will solve your problem.
Altezzas typically oversteer; I'm not sure what the problem is there. It also comes standard with a 6-speed trans (though not adjustable), so that's really not the problem. The other Altezza drivers are pretty aggressive, which makes it hard to stay away from them. The best I can say is try Turbo 2 and a 1.5-way (or full race) LSD. Try the racing or sport suspension, too, and lower the car a bit and boost the stabilizers. The Altezza does tend to lean like an ocean liner.
Definitely go with slicks as F1king suggests. If you can't make it on super slicks, go to mediums. They will last a 5-lap race without needing to pit.
Keep it up! These are both considered difficult series due to the freight-train driving style of the competition.