I sent a case-specific enquiry asking for urgent processing as I am travelling. This is the response I got:
Thank you for contacting Citizenship and Immigration Canada.
New Permanent Resident - No Possibility of Urgent Processing
This message is to inform you that we have received your request asking us to process your Permanent Resident Card (PR card) urgently, but that there is no urgent procedure for new permanent residents.
If the card is not ready before your departure, you will have apply for a Travel document (permanent resident abroad) at a Canadian visa office located outside Canada before returning to the country. The application is available on our website. You can fill out the application online and print it or fill it out by hand. The travel document is normally valid for one entry.
Please note that a PR card or travel document is required for all permanent residents returning to Canada on a commercial vehicle (plane, train, boat or bus).
*sigh*