With regard to the bank stuff... My wife called her bank to ask if we could open up a joint account, and after initially saying no, they checked around and eventually said it was possible. When we went in to open the account we had to bring along photo ID (obviously) and proof of residence -- for the latter we brought our apartment lease, but they didn't even look at it. Never left our folder!
I completely understand how daunting it can be, especially if rock solid cohabitation documentation (i.e. Hydro bills) are hard to come by. Creating a narrative through a letter of introduction and/or explanations on attached sheets will help. For instance, if you're not on the lease but pay rent through something like, say, Paypal, you can go ahead and explain this while also including a printout of all the times you've transferred money to your partner. If you've ever texted with the landlord over rental space matters, screenshot those texts, paste them in a Word document, and print it off. (Even though I was on the lease, I did exactly this.) Have family members and friends attest to the fact that you do live with your partner. In short, all sorts of creative ways to show cohabitation and prove genuineness of relationship. View all the bits of evidence in whole, not in isolation.