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Given that your park skis are probably ~80mm in the waist, and given that that's what we used to consider a fat ski (86mm was super fat, AK Rocket style), they're fine. I don't have park skis anymore unless you could old Line Soul Rebels (my rock skis) and those handle the pow very well obviously what with them being Pollards. But even so, I remember skiing a knee deep day on centre mounted first gen AR5s in Whistler (very heavy snow) and the only thing that bugged me was the mounting point.
Basically, park skis aren't the issue, it's the centre mount that can cause an over the handlebars type of feeling and you end up backseating a lot more to compensate. But you can adjust for that.