Your description almost screams for a narrow-ish ski with reverse camber in the tip and tail.
Reverse camber in the tip and tail makes a ski feel 10-20mm in soft snow IMO. Also makes it super easy to butter. Downside...sketchy at high speed and/or on ice (and you ski east coast, I never have but I hear its pretty firm over there).
Any ski is going to be a bit of a compromise but Salomon 2012s, Moment Rockers, etc... come to mind straight away.
There are other skis such as Armada Halos, ON3P Blue Steels etc... that might fit.
But back to a ski being a compromise..thats what they are.
If you ski a lot of bumps then I'd be reluctant to recommend the 2012s and Rockers as they're too wide IMO. I had '10-11 Rockers this summer at Whistler. Great fun on slower jumps (best ski for learning butter tricks I've ever tried too) and for screwing around in the bumps but they were too soft for the bigger features and too wide and too soft for a serious attack at the moguls.
On the other hand a narrower ski like the Halo's are not going to be as good in the soft stuff but would probably work well in the bumps. I was surprised by how beefy the Halos were which might make them good for firm east coast snow (but worse in the soft stuff) and going for it in the bumps.
You mentioned price in your post. I think that you can get Alphas from previous seasons (I don't think the changes from the last years to the coming seasons Halos/Alpha's is that much). If so they're bound to be a good deal. Last seasons's Rockers were much stiffer (apparently) so might work as an east coast ski to your description too.
PS The only rockered ski I can talk about with a lot of experience is the the '10-11 Rockers. I do have a lot of experience on rockered, multi-sidecut, reverse-camber, etc...skis but they're mostly pow skis rather than park skis.