Lepidoptera can articulate all their tarsus much like you can your ankles and toes. They individually can be damaged and rendered inopperable same as yours can. If they are not damaged, underdeveloped, or were not feed something they shouldn't have been, its more likely an infection that could be viral, bacterial or parasitic. Whatever the cause, if they become unusable to the point that an imago can't complete its assigned task on its own, the humane thing to do is euphanize them and move on.

So then they can manipulate the hooks so they point straight or down. I fed it Gator-Ade, and tested it for OE, which came up negative.

If the disability appeared coincidentally with the feeding and has nothing to do with my handling him -- and I can't figure how I could've hurt him in such a way that one minute 2 hooks worked and the next none worked -- then perhaps an infection set in and just manifested at that particular moment, even though he seems healthy in every other way. Does that seem possible?

In the event that it is an infection, I will feed him for a few days to see if things improve. I have nursed many a sick Monarch back to health -- even those that were almost dead, none with OE. I'm not all that hopeful that things will change, but it's worth a try.

Someone else suggested to me that if there was any residue of flea treatment around, it could cause problems for caterpillars. I don't allow any treated animals anywhere near my critters, but I wonder if there was even a whiff of it around if it could affect the butterfly in this manner. Any thoughts?

Gatorade has mineral salts in addition to sugar and water. No more Gatorade, just sugar & water, for a day or two. See what happens. That is what I would try.