I do want to hit on how important the 4457 is to a US national. You cannot bring the gun home without it. The Canadians probably won't let you leave it behind. Plus under the ITAR (international traffic in arms regulations) law in the US you can't leave it behind. So you are stuck in limbo if the 4457 is lost, defaced or cannot be read. Remember, customs does not keep a copy. Did you keep a bill of sale? Will someone fax it to you? Not a place you want to be. Been through this wringer, not with Canada. In African countries the 4457 is viewed as a firearms permit, card or whatever. It is easier to replace a passport than this little piece of paper when outside of the US. Laminate it (some say this defaces the document) or keep it in a baggie, with passport and health record (I do not want to get shots in an African airport).
Now if you want to get a major caliber handgun into the great north, become a competitive shooter. This is second hand from my son, but forgiving the acronyms, shoot USPSA in the US, it is under the IPSC that holds matches in Canada. They held a championship match in Manitoba last week. The ATT should be granted, but it may be shortest route, shoot and get out; I don't know. You will not fake this, you have to qualify. It is like an RV, gun, sights, gunsmith work, reloading set up, and 1,000 to 5,000 rounds a week. It is hole into which you throw money, but as an RV fans we should understand. So, if you follow this route it is like an RV, airplane or race car. Don't blame me when you are too broke to buy a new camper.
There are probably other ways, such as police shoots and so on, but it ain't worth it, unless it is something you are going to do anyways. Plus, do you want to be an American, that shoots a Canadian in Canada? No matter what kind of guy he is, you are most likely to have a very interesting story to tell! In 10 to 20.