Two words: Keep practicing.
More lenghty response:
I am not convinced (in fact, I seriously doubt) that you are actually 'carving'. It sounds like you are pretty proficient riding on an edge and controlling speed by side slipping - which is great for a beginner.
But you state that you have problems turning. That points to a technique issue, especially since you are riding on a soft, full rocker board that will start turning pretty much as soon as you think about it.
You should read snowolf's description of basic skidded turns and watch his videos. Then practice on runs where you are comfortable, paying particular attention to your technique. Continue to challenge yourself by gradually moving to more difficult terrain (steeper greens, blues, etc.).
Once you can get down blue runs linking turns without any problems, you should be able to at least navigate a black run - you might fall occasionally, mess up some turns, or have stop sometimes but that is ok, it is part of progressing.
Then you can also get into dynamic skidded turn and basic carves - but make sure to get the fundamentals down.
Back to your original question: Yes, any soft rocker board is going to feel less stable and more squirrel-ly when flat-basing. However, if you are having problems with this even at slow speeds and in relatively flat sections, then it is a rider/technique issue not a problem with the board.