Hi Pierre, I actually went through a similar situation when purchasing my aircraft, a 1970 M20G. I'm a Canadian citizen, but I live and work in California. An N-numbered aircraft must be registered to a U.S. entity, be that an individual, corporation or trust. The only exception is a Non Citizen Corporation can register the aircraft provided that at least 60% of the annual flight hours will be within the U.S. (this is the route I took). In your case, the only option would be a Trust, where a bank here in the U.S. would be the legal owner of the aircraft and you would be the beneficiary. You would need to hire a lawyer to draft the trust agreement and in most cases you would pay a monthly or annual fee for the services of the trustee.
The FAA had temporarily suspended processing foreign owner trust applications, but it appears they have resumed them (http://www.ainonline.com/news/single-news-page/article/faa-no-ban-on-registrations-of-foreign-owner-trust-aircraft-25223/).
In terms of financing, I think that will be the hardest. I was very fortunate not to have to finance the purchase of my airplane since I was unable to find any lender that would lend to a Non-U.S. Citizen despite having a good credit score in the U.S. and no Canadian lender was willing to finance the purchase since it would be stored and registered outside Canada. I have no experience with Aircraft Guarantee, but it sounds like it could be an option worth exploring, although it's unclear on their site if they just act as a trustee or will provide financing as well.
I converted my FAA PPL to a Canadian one painlessly (20 question written exam), but haven't converted my FAA IFR to a Canadian one yet although it's a similar exam. I know a lot of people who trained here and converted to JAR easily... so if you wanted to convert your JAR PPL to a US one, you could come here do your IFR easily.
Let me know how it works out for you. I'd recommend getting the following book - it covers Non-U.S. Citizen aircraft ownership in greater detail: http://www.amazon.com/Aircraft-Ownership-Legal-Tax-Guide/dp/0071407642
-Andrew