All ice is not created equal. If you had all-season's that were "more than adequate" on ice then you were never on ice that was much of a challenge.
Get winter tires for the months that are cold enough to run them. I would not suggest you get winter tires that perform the best in ice/snow but rather, those that perform the best on cold, wet pavement. They will still outperform any all-season radial by a dramatic margin on ice. e
If cost is your concern, consider that for the months your car is wearing winter tires, your summer tires are staying nice and not taking any wear. So, while it does cost more to run two sets, it's not that much more and it's cheap insurance when the nasty hits. I'm an excellent snow/ice driver but, on public roads, no one is invincible and especially if you're on all-season radials, you are even further from being invincible. If you didn't have to deal with the hazards of oncoming traffic, drinking drivers, drivers on medication, inexperienced drivers and reckless drivers, I would say you can probably get to your destination just fine on all seasons and, if the nasty hits, just slow way down, unless it's really bad you'll probably make it. But driving in the winter dark and wet with puddles and lurking ice, you will be glad you have the winter traction. If for nothing else, to avoid the idiots trying to take you out. The danger isn't when there is an ice storm (because then traffic is reduced to a crawl). The real danger is when everyone is splashing through the winter slush and puddles at high speed.
What's your life worth? Alternatively, how much would you pay to avoid 6 months in rehab/physical therapy.