Personally I wanted some of the same as what you are looking for and went for a Rome Mod Rocker. Flat based with raised tips and it seems to be quite stable when I want it to handle carving/freeride, but also ollies like crazy, lands off sidehits pretty catch free even if I land off balance.
Handles moguls/tight trees well too. Love the damn thing!
Was also checking out a Ride Machete which is similar and have heard the Capita Indoor FK is good too.
The Mod Rocker and the Machete both look like just what I am looking for. Hopefully one of them will be available for demo.
It looks like these boards are flat between the bindings and raised at the nose and tail. So, are they considered rocker-flat-rocker?
It looks like the Never Summer Proto CT gets thrown into this group of boards as well. Any reason I shouldn't consider that one too?