I did
exactly the same thing. I was at least fortunate to have a backup (that second US passport - for exactly this situation!) I gave them a US Express Mail prepaid envelope (not sure why they wouldn't let you use the global priority prepaid envelope for shipment back to Canada) and had it sent to my company's US office. USPS took two days to deliver a "guaranteed overnight" envelope.
FedEx with Saturday delivery worked, which is why I got my passport and COPR back yesterday and landed less than 4 hours later.
Good luck with getting your passport and COPR back and enjoy the sweet success of your landing!