What Ski, what do you really want to learn
Two things, you stated that you wanted to improve your carving. That would be a great thing to tell the instructor or the Ski School Supervisor that its something you want to work on. Being a USSA guy I'm not that familiar with the current PSIA levels but I believe you start learning to tip the skis at level 7 and really get into it 8 and 9.
As for your question, based on your penchant to start carving a bit more there are a host of good skis to consider. They would all fall in a all mountain/carving ski category.
Rossignol ZENITH Z1 TPI
Nordica Speed Machine
Just to name a few. If you search the Equipment section for types of skis (Carving, All Mountain, Fat) you'll find threads on just about all company's current offerings.
Oh yeah, I scored a Level 2 on that cool Aspen/Snowmass level-0-meter