Hi tabbycat, and from Vancouver, welcome to MobileRead.
As you mentioned, you usually have to physically go to a library to get an actual card and number before you can borrow online.
I have two library cards, from two different local libraries so I am lucky.
Since I live in BC, I can only suggest the British Columbia libraries that lend eBooks, all from the following province wide site:
http://bcpl.lib.overdrive.com/B45914.../Libraries.htm
Not much help, I'm afraid, if you don't live in BC or near one of these libraries.
If you tell me which province you are from I'll try and search out the closest eBook lending library to you, and also look for any eBook lending libraries in Canada that will accept new applications online (if there are any).
WDE.