And man, it made an amazing difference. I had almost none of the initial instability that I usually have right after putting my skates on. I stopped needing to use my arms for balance. And I remembered the foot crossing-over trick that I had figured out a month ago and then forgotten.
About halfway through the evening I decided it was time to start learning to skate backwards (after all, I lack ms_nico_blue's clever "my health insurance doesn't cover this" excuse). I spent a while thinking about how to best go about the learning process. Some recent reading I've done about brain development suggests that when re-learning the use of limb after a stroke, one of the most effective techniques is to put the functioning limb in a sling (!) and then force the patient to muddle through everyday activities using the damaged neurons. Their motions start out awkward, spasmodic, and vague, but as long as they have some tiny measure of success, this technique frequently causes them to recover nearly all the grace and fluidity they had before the brain damage. So I decided to try a similar thing: to go to the practice area at the side of the rink, point my ass in the proper direction, and not let myself turn around until I had reached the other end.
In about 10 minutes, I made it, using a bizarre kind of body-flailing and foot-stomping that even the most generous lexicographer would not call "skating". I was exhausted and took a break, but I returned to it a few more times, and by the end of the evening I had made a grand total of 6 traversals.
I believe this hobby is entering the familiar "obsession phase". My current plan for tomorrow is to sneak off from Thanksgiving at 7pm and go skate some more :)