Here are my thoughts and I hope you find something useful.
(1) The absolute easiest has to be friends or family in Canada or elsewhere who can be your "beard".
If you just don't have the trust for something like that because of the money involved you could consider option #2.
(2) Increase your expenses and perhaps rent something very inexpensive in one of these countries. The ID issue would worry me there for any cashouts. You need a driver's license, etc with this new address in a foreign country. I'm not sure of the snags on that.
If the problem, what is the other way and one needed to move to the U.S. to gamble, that would be a big problem. How many guys are swimming through the Rio Grande to just live in the U.S.?
My point just being that for any country and that probably includes countries like Canada, it isn't just a matter of showing up and living there. If moving to Mexico is as easy as telling the immigration official at the border "I don't like the rules at home, I'm moving here". And the guy goes "OK" that is a good spot. You will get all of your business affairs in order easily but if not, I think there is more to this idea that needs to be thought out.
(3) Can you afford a vacation home? How about a bachelor apt in Bankgok, Denmark, Canada, Mexico, go there a few times per year or once a year or never.
But you need the ID's and utility bills that you do have a residence there.
And from your U.S. home make use of technology to bet from an IP that isn't located in the U.S. and is located either in the country of your vacation residence or even a computer right in the vacation home. That may or may not be necessary. Better if it could be.
