Thanks for starting this discussion. Lots of interesting stuff here, and much food for thought.
Some of the comments posted above remind me of a mountain bike race I was involved in a few years ago. The 24 Hours of Moab is a relay race that lasts 24 hours (hence the name), from noon on Saturday to noon on Sunday. The course has several challenging technical sections that were somewhat intimidating for me during my first lap (during the afternoon), requiring consecutive moves over big rocks and drop-offs. (I'm much more scared of falling off my bike onto rock than falling off my skis onto snow.)
Unexpectedly, these sections were actually much easier for me during my night laps, since my headlights really could only illuminate one small part of each section at a time. Not being able to see the whole thing, and being only able to focus on one small piece at a time really helped. In one section, I cleanly rode over a huge drop before I even had a chance to realize that it was there. My body knew what to do and just reacted, functioning better without too much interference. (I need to remember this more when skiing bumps.)
So, I think you should sneak out and do those long hard icy runs at night, with a headlamp. (Just kidding.)
As mentioned before, The Brain is just doing it's job, and trying to keep you safe. When you are skiing, Danger is perceived as being down the hill, since that's the direction of gravity and additional speed. So, in response, when we start becoming uncomfortable with our speed as we move into the fall line, our brain causes us to try to move away from danger, by leaning back up the hill, which is perceived to be a safer place.
Unfortunately, when we do this, we remove pressure from the outside ski, which is precisely where it needs to be in order to turn out of the fall line, and hold more effectively on the ice. By trying to move us away from Danger, The Brain actually makes things worse.
One exercise that I remember that was very helpful for me was to "shake hands" with Danger, actively reaching down the hill with my hand (outside hand) as I approach the bottom of the turn, as if shaking hands with the gravitational force pulling me down the hill, rather than moving away from it. This keeps the pressure on the outside ski, helping to bring it out of the fall line, and maintain the pressure necessary to hold on the "frozen granular" surface.
To get the feeling of this edge hold on something less intimidating, you could try pulling off to the side of a trail near the bottom of an icy pitch (in a place where you are clearly visible, and not in danger of getting submarined by others sliding down the hill as if in some bizarre human video game), and try side-stepping up the hill a few feet. This should give you the feel of how to pressure the edges properly to get them to hold. When you've taken a few steps up the hill, with your skis still pointed across the hill, you could then practice alternately flattening (sliding down the hill) and edging (coming to a stop) the skis to get the sensation of how much control you really do have.
Having skiied in the East for several years before moving West, I chuckle now when I hear people complain about the "ice" out here, remembering a day a Mad River Glen where I skiied around a section so clear, blue, and frozen that you could see last year's trail maps and petrified Snickers bar wrappers entombed about half way down in the ice. Also remember falling on Ripcord at Sugarbush on a particularly bullet-proof morning, and sliding a long way before being able to come to a stop. So ... I feel your pain. But I certainly don't miss it.
If you're interested in doing some additional reading on fear and the mental aspect of skiing, I seem to remember that Gallwey's "Inner Skiing" had some stuff that you might find interesting. Or, you could just move out West.
Hope that helps ...