hapi, your dilemma is interesting. I assume you're working at a U.S. company or at a place with similar hierarchy/corporate structure. If you're in the U.S. right now, I suggest that you approach your HR and your supervisors the following way - "hey guys, there's this thing called EB green cards that you can sponsor me for. I need permanency in my life. As of now, I am vulnerable to arbitrary changes to the country's immigration laws. So I am exploring Canada's skills based green card system where they give green cards to highly skilled people. This is a long shot for me but I need a letter from you guys verifying my employment and job duties. Please make sucha reference letter available to me asap" (undertone at this point - they are legally required to issue such a letter).
The above approach should work for any other place besides thr U.S. The key thing is not to antagonize your current employer. The next thing to do is to subtly make them understand you're bargaining for a better pay/position. Finally, you should stress that this Canada application takes over a year to process and thst you're just throwing out an application just to see how it goes and that you have no incentive to move unless you find a similar position there (throw in some jokes abt your cousin or uncle working at a restaurant in Toronto and how they're telling you it's not worth it). Just humanize your situation and be honest abt what you're doing (well, don't be too honest, pepper your story witha bit of melodrama like I suggest).
Best wishes to you.
