Thank you chipits and rachiy for your helpful advice. I spent a lot of time researching this today and after much frustration on the CIC website (what a surprise) I also came across the restoration of status avenue on the forums. I'm so grateful, yet again, for the collective wisdom of the forum. If I was relying on CIC-produced information, I would be lost.
In case anyone else needs this info in the future, IMM 5558 (document checklist) and IMM 5708 are the documents to fill out. This is the same form that would be used to extend your stay before you actually overstay (by far the best route). The application fee is $200. The word is, however, that the forms are processed very slowly. The time frame I've seen mentioned is 16 weeks. Ironically, it's quite possible that I will get the PR before the application to restore my status is processed.
The good news seems to be that as long as I submit a complete application, I can stay in the meantime (implied status). I intend to submit this ASAP. I've never, ever overstayed anywhere in my life. I'm mortified!