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Well you have the K2 so why not just add a good carver to the quiver?
To expect a park ski to carve really well is a lot....yeah sure when they are brand new and you can maintain a good base and sidewall angle sure....but when you grind the edges underfoot it just won't carve well because it won't stay tuned and you don't want it to be anyway because it would catch constantly...a ski that hits rails and carves well like a gs ski can't really exist.... You can carve on a railled park ski, but to say it carves well is a stretch.
Add a ski to your quiver and keep it tuned...Shamans carve hard. Maybe a pair of jeronimos or ar7 you can carve on for a while and then once worn you can use them in the park...
You are on this website so you must ski....having a quiver of two is very modest....
Sharpening your edges will inhibit your rail skills in the park, have you ever hit a rail with sharp edges? ouch. Not to mention you increase the chances of ripping out an edge) You could bevel the base edge angle to 3 degrees however it will not engage turns quickly or even hold an edge as well. Your K2s aren't the best carvers even with a good edge on them so just keep them for the park an don't bother tuning with them ever again.
What I am trying to say is that a good twin tip can carve with good technique and tunning, however when you rail them don't expect them to carve exceptionally well. You can't expect a ski you hit rails in the park with to hold an edge like a carving ski... Furthermore, if you want a good carving ski it won' t be a center mounted twintip....
I am assuming you actually hit rails in the park.....umm....well if you just want a good all mountain twintip to land switch and still carve moderately well check out the On3p Jeronimo....