...competing with hundreds of other 200 hour pilots that have the right to work in Canada for longer than 10-12 months, I might add. You're at a disadvantage from the outset, since a company wouldn't want to invest money and time in training you, knowing that you'd be leaving in less than a year. (And some friendly advice - do not offer to pay for your training; that's simply "not done" in this part of the world and will get your resume sent directly to the garbage bin.)
Your best bet may be doing an instructor rating, and then instructing at that same school (this is how many instructors get their first jobs) - but of course, they wouldn't be able to guarantee up front that they'd hire you, so it would be a gamble.