Lost my mobile authenticator, might this work?

[lordjust]

It's my account but i'm an idiot that decided to put US as a country rather than Canada

Did you already try the "I lost my authenticator and I want to remove it from my account" button? If you can't find your phone that's the only option you have. If you call or write the support they will just tell you to go to the website and use that button. I never tried to remove my authenticator so I don't know which informations they want but that's your only option. I don't know if they look at the country because you know you could just moved from Canada to US and back or so.

[Cyclone Duke]

It's my account but i'm an idiot that decided to put US as a country rather than Canada

Your registered country doesn't matter. Submit ID in your name is all that matters. It doesn't need to be from your registered country.
Also you can change your registered country by submitting proof of residence in your name (utility bill such as electric/gas etc).

CD keys are NOT shareable, they are a one-time use type thing, on a resold account though, that is a whole different can of worms. Keyloggable? really? That is extremely unlikely on older accounts, like the situation I described above. And yes, they would be evidence you are most likely the owner or at least someone who knows the owner. Like I had said above though, it won't be the ONLY thing they ask you, but its one thing that will help your case where you won't have to snail mail your driver's license.

Oh god, snail mail? You take a photo of your ID and submit it digitally online, not by snail mail. And CD keys being sharable as a means to prove ownership - not re-using to create multiple accounts I meant.

[Deleted]

There is no other way other then getting your phone back or mail them some ID, the country you are from is irrelevant, I have my country set as UK so I can take advantage of all promotions, but I'm not a British citizen.
However, if you added an authenticator to an account that wasn't yours to start with and that's why you have no ID to give them, good luck finding your phone, otherwise you're about to face an uphill battle.

This is one reason why I went with physical authenticator rather than mobile.

Well, there's pros and cons for both really, you can't accidentally format the physical one, and you can just have it glued to your monitor and "never lose it", but your back sticker can get unglued (happened on mine) and you can lose it or someone else can take it.
The mobile one can get lost as well, you can format, people can also get a hold of it. But it's easier to backup, and you can have it on multiple phones too. In my case, I just made a Titanium Backup(Android phone) of my authenticator, and have it on an encrypted .rar on my Google Drive, so it's accessible everywhere if I lose my phone.