And just to reply to my own inquiry, I did call CX and they were able to waitlist me for business class on my paid economy fare. The agent referred to it as an "exception" but I think he was just confused and wanted to set my expectations before he called a supervisor to get it done. The agent said I'd get an email if it became available.
The only wrinkle is that I am waitlisted for the highest booking class (J), when I would have preferred to waitlist for a lower one. So if you do that, try to specify the booking class.