Not totally sure if it would work better, but keeping with the K2 theme the Darkstar might not be bad to check out. It has flatline rather than a form of rocker, so it's a bit like a cambered board when you're on ice (which is better than being on a rocker board). It's a bit more all-mountain than the parkstar I believe.
Now, if you're on ice a lot, you might want to consider some other companies that use magnatraction or some variant.
NeverSummer Evo has vario grip which should help with some of the ice. It's also reverse camber rather than a form of rocker, so it's a bit more stable. They used to be pretty stable too, but I'm not sure if they've lightened up a bit on that aspect.
Mervin (Lib-Tech, GNU) has some stuff. I don't know much about them to be honest. I'll let other people talk.
Smokin Snowboards 2010-2011
Good boards (from what I've heard anyways) that usually have magnatraction.
I believe YES uses something similar to magnatraction (or is). Burton also has their own tech, but I'm not too familiar with their line besides some of the more famous models.
Do you need magnatraction or an equivalent? No. Would it be nice on ice? Depends, some people swear by it, some hate it.*
Anyways, that should give you a bit of range to look at. Other people can certainly describe more about the individual boards (most with some personal experience probably). Hope this helped a bit!
*Smooth Side, Smooth Ride in my opinion