Help in the steeps

you seem to be making contradicting statements in your description of the problems you're having.

You say the skis feel hooky and when you drive the tips, you almost crossed your tips...yet you say there's no tip to engage on the S3.  If you're getting hooky tips, wouldn't the opposite be true?

You also say the ski would not hold an edge real well, but you're getting a lot of chatter and sliding, which are actually 2 opposite problems.  Chatter is caused by sharp edges constantly grabbing ice and then releasing then grabbing.  Sliding is caused by dull edges.  If you're chattering, it's because the ski edges are being overloaded.  This can be caused by hammering on the edges too hard on ice without giving time for the pressure to build up.  Obviously this is very easy to do skiing steep icy terrain.

My guess is that since these are new skis, perhaps your old skis were not tuned very well and so you're used to dull edges.  The dull edges allow you to slide/butter a lot easier.  The new skis with sharp edges will be grabby and cause you to feel like the tips hook, as well as chattering if you're not easing the pressure onto the skis properly.  Both these issues can be resolved by getting used to skiing on well tuned equipment.  Some tweaks to technique may be necessary.  You may also choose to detune your tips/tails to reduce hooky feeling (though you'll lose out on being able to engage your tips as quickly when carving on groomed.

As for the contradictions..you're probably just getting some terms mixed up.

I have skied the S3 in Taos on some of our steeps, when they were hard but not icy  and did not notice your issues. It felt stable.

You may just have to get used to them or it may be that the factory tune has you hooking your tips. 

while bringing the skis in for a tune is always a good idea since the factory tune may or may not be a good one, I don't think it's going to solve the problems you describe.  You usually ski in soft snow on dull edges.  The situation you described is basically the complete opposite.  Just ski on tuned equipment more to get used to balancing on a ski that holds an edge instead of slides.  Practice clean railroad track carved turns on groomed to get used to that feeling and also learn to progressively engage the ski edges.  It helps develop offensive movements (guiding skis in direction you want them to go) rather than defensive movements (throwing tails of skis out to control speed).  Chatter is generally caused by defensive movements on icy slopes with well tuned skis.  Not doing that in steep icy conditions is easier said than done, so perfect it on flatter terrain and hope some of it carries over. 

An easier approach would be to just shoot the chutes instead of trying to turn so much in them.  ;-)

You shouldn't be making turns til it opens up anyways.

Would agree with Majortato on the defensive move (straight lining icy chutes, is a personal choice ;) Sounds like you could be going from a jump/lift to a hockey stop, where the jump or lift is your edge release. A flattening of the skis followed by edge engagement, and whole lot of leg steering so your carving a very short turn while keeping your skis on the snow and still facing down the fall line, is far more stable. (I'm assuming the chute is wide enough to make a turn.)

I'd say practice on single black terrain, keeping skis on the snow, and making short turns. Concentrate on shifting your weight down the fall line to release the skis with no lift. You should be facing down the fall line, and using your legs to guide your edges through the turn. If you find yourself going too fast you're probably either standing too tall or too short to get fast leg rotation; or, not finishing the turn, be patient. If your getting a lot of tail skidding, you're probably rushing the turn and pushing the heels out. (also look where your uphill hand is if your tails are skidding. If its low and/or back... your over rotating. keep that hand in view.)

Frankly, IMHO, icy chutes at 50+ degrees are best viewed from a distance.

This sounds like expected behavior for rockered skis. Rockered tips are supposed to offer "friendlier" turn entries. This means they won't be as clean when trying to do arc to arc turns. That won't apply in steep chutes, but it would explain the WTF crossed tips feeling. Without a clean start, there's less turn to spread the pressure over. With less effective edge, there's less edge to spread the pressure over. With too much pressure, there's going to be chatter.

The question is: is there a technique adjustment that can accommodate for the equipment design change? It might be possible that a skiddier turn entry instead of trying to drive a floating tip will solve your problem.

 I'm finding with an early rise shovel I need to be more positive in making certain my new inside ski edge angle matches my outside ski edge angle from the very beginning of the turn.  So I need to release the old outside ski edge to begin the new turn rather than immediately pressure the new outside ski.

Interesting thread as I've not skied rockered skis yet.  To me, what you said makes sense.  From what I gather, these rockered skis allow the skier to pivot quickly, even in powder.  It sounds like the OP when trying to engage the shovel edge, he's instantly moving right through the movement into a pivot by default and crossing the ski that hasn't been fully tipped or pivoted yet to match the new downhill ski.  Scary stuff really, especially in a steep/tight chute...eeeek!  Sounds like hoppy hockey stops will be the rage, I think it's called progression.