I had what seemed like a pretty good idea for staking --
which was to use the hollow foam insulation tubes people use to insulate pipes as my stakes. They're strong enough to hold plants up in reasonable amounts of wind but flexible enough not to introduce new kinks; they're slit down one side, making it possible to slip one on around the petioles without further damaging it (though that did take two people to do); and they're fairly cheap.
Unfortunately, it appears that this idea came too late to be helpful. The A. bulbifer appears to be producing a new bulb, but its petiole was pretty badly damaged and the leaf is severely wilted (worse now than in the pictures), and it's not clear whether it's going to be able to finish making the bulb before the leaf dies.
The A. konjac was also more badly damaged than I had initially thought, and I suppose the process of wrestling it into the insulation tube probably damaged it further even though we were trying to be careful. The wind has also blown hard enough to shove the petiole through the slit in the insulation a few times. (I should have taped it up once we got the insulation on; I didn't think the wind would be strong enough to push it through.) So it's probably just dead, and the plant will have to carry on through the three bulblets it produced this year. Which is not so bad, as consequences go. I suppose I've learned a valuable lesson about putting Amorphophallus outside as soon as it starts to sprout.