An update on this story.Bossman sent his contact at Company K an email later that week (after I hounded him each day to do so), to which she replied that lessons would not continue after the contract expired in December. That was that, as far as BM was concerned and he decided to drop the issue.
Three of my four Company K classes are my favourites classes overall, not to mention a significant part of my monthly income, and I wanted to see them continue so I went straight to the top. That's right, Power Woman again (she's in my Thursday class at Company K).
On 21 Oct, She asked me if I had heard about lessons continuing and I told her that Mr D's Secretary (the person we thought was in charge) had told Bossman that they wouldn't be. PW responded that that was incorrect, as Mr D was only a second level manager and that the first levels were still discussing it. She said that she wanted lessons to continue and would talk to her boss (one of the two first level managers) about it. I smiled, because I knew that after she talked to him, lessons would be continuing.
BM received an email the following day asking him for a proposal for six more months of lessons, which he sent on 25 October after asking me if I had had anything to do with it.
On 29 October, an email was sent out to the students in the classes taught by our school telling them to call the personnel department only if they didn't want to continue lessons. All four of my classes will be continuing, Tall Colleague's class won't and Secret Smoker's class might be if they can find one more person (each class has to have at least three people and one in her class of three won't be continuing).
I'll probably have to go through the whole process again in July.