Upvote:3
Well, after a couple of calls to the CIC Call Center (+1-888-242-2100), all I need is a photocopy of my current study permit and a photocopy of the application form that I'm using to get it fixed. I might have interesting times at the the customs, but apparently it will be OK.
The important point here is that regardless of whether I physically have the study permit with me or not, I still have a legal status in Canada.