The situation I was in was most like the high speed wheel touch described by Toyman991; the front wheel was shimmying fast and violently, say 2-3 cycles per second. The bars were shaking me like a dog shakes a rat, couldn't see more than a blur and don't think I could have steered the bike anywhere until I got the shimmy under control. But it wasn't getting any worse, and I had time to realize "hey, maybe I can get out of this". Chose the wrong way, though.
The geeky side of me wonders if this was a lesson in precession, like what happens with a spinning top after you knock it- goes unstable and eventually tips over.
The suggestions of going loose with upper body, braking carefully with the rear brake only, and getting feet down make the most sense so far. The instant I started braking (with both brakes) the shimmy got worse until the bike jacknifed.
Great ideas, guys.
-Bob Norris