UPDATE: After I filed a DMCA counter-claim, and following about two weeks of being blocked, the video was finally reinstated. Yay. According to Google, the process goes like this:
After we receive your counter-notification, we will forward it to the party who submitted the original claim of copyright infringement. Please note that when we forward the counter-notification, it includes your personal information. By submitting a counter-notification, you consent to having your information revealed in this way. We will not forward the counter-notification to any party other than the original claimant.
After we send out the counter-notification, the claimant must then notify us within 10 business days that he or she has filed an action seeking a court order to restrain you from engaging in infringing activity relating to the material on YouTube. If we receive such notification we will be unable to restore the material. If we do not receive such notification, we may reinstate the material.
Note that I have not (yet) received any apology from any representative of SpecialtyAutomated for incorrectly issuing a DMCA notice on Youtube, or an assertion that they are not connected with whoever issued the notice. If I receive one, I will post an update in this space.