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If you want to tour and ski park, I wouldn't choose the Barons. Not only are they heavy, but they also put you high off your skis (36mm Stack Height). If you want to ski park and be able to tour without the need for a quiver, you've got a two options.
1. BCA Alpine Trekkers. These put you high off the ski for the uphill, and feel considerably more unstable than AT bindings. However they do allow you use your regular alpine bindings for the downhill, so that is their main selling point. If you are going to be purchasing Trekkers, I'd choose your bindings carefully, they don't interface well with Rossignol/Look PX bindings due to the high heel piece. Also they don't interface well with the Rossignol/Look Pivot bindings due to the fact they don't engage the break and the high heel piece may cause problems (can't verify the high heel piece problem as I haven't personally used Trekkers with a Pivot series bindings). Although I do know that the break 'engagement' problem can be combated by winding duct tape around the rail of the Trekker, so that it engages the break.
2. Your other option is to use insets either Binding Freedom inserts or Quiver Killer inserts. I haven’t used either, but from my ‘lurking’ on TGR, I am aware that Binding Freedom inserts are superior; also that the guy who designed the system runs binding freedom. I’m not sure what it’s like to ski park with inserts, as it’s not the most common use for the inserts, they tend to be used more frequently by backcountry skiers. However there are probably a few guys on here who can comment on how they hold up in the park.