I started with the simplest bit of advice I was given about working with Libby's back feet... the first one mentioned in the previous post. On my asking-for-advice post, someone left a comment saying the same thing:
"Make sure the horse is balanced to start with, then you ask for the foot for 1 second - YOU put it down. 2 seconds, 4 seconds, etc, and work your way up to a minute or so. The decision to put the foot down is ALWAYS yours. Spending some time each day working this way should help to solve the problem."
So I tied her, used the pick on her front hooves, and then picked up a back foot and instantly let it down, praising her profusely. Then the other back foot. Back and forth I went, counting to two before letting it down, then four. By the end of the session I was actually able to pick her hooves with the hoof pick (hastily, because I wanted to be the one to decide when her foot was going down).
I'm partially at fault for her behavior, because I haven't faithfully handled her each day like I should have. It was so awfully hot for so much of the summer that I dreaded doing anything, but I know that's an excuse; it's just easy to put things off, that's all. I'm making a new resolution to handle Libby's feet every day. It only takes ten minutes or so.
And for Guy, who also left a comment with advice: if it turns out to be a balance problem, I will surely try your advice. In fact, I need to be putting all four of her feet up on something once in awhile so she'll be used to it when the farrier comes. Thanks for reminding me.