1. your partner could add you on her credit card without you even be present...i live outside Canada with my partner; he have never been to Canada but last time i visited Canada i called the bank (TD Canada Trust) and add him on my credit card; noone asked me for anything; all the work was done by phone; i don't know what is the procedure for other banks but give it a try; since you r not the main user of the credit card it should not be a problem
2. also she could add you on the apartment lease but that depends on the landlord; if he sees you every day and you r in good relations maybe he will not ask you for any ids
3. lastly, my parents added me on the Hydro bill and again noone asked any ids...many of these procedures are done over the Internet; try them all: Gas, Hydro, internet/cable/phone company
4. also, do u have a mobile phone? doesn't the mobile company send you letters, bills on your name to that same address your sponsor has? those r good too
really u should get your valid passport ASAP
i don't know from what country you are but i know in some countries (Middle East) they might not issue passport unless you do the military service or they would issue it for a short period of time; if that's your case and you cannot go to your home country, try to get a working visa somewhere else, have a valid status there and your sponsor could apply then outland for you; you don't risk being arrested and outland applications are usually faster than inland
good luck!!