So do you simply live in Canada or are you a Canadian citizen looking to move to the USA?
Here is a link to Amex's website regarding moving internationally:https://www.americanexpress.com/global-card-transfers/
"To be eligible for a Card transfer, your Consumer Card must be issued by American Express. You must be the Basic Cardholder, and have held the Card for at least 12 months. Your Card Account must be open and in good standing at the time of the transfer request, or if the Card was previously cancelled by you, it must have been cancelled within the last 3 months. (Corporate Cards, International Dollar Cards, Global Network Cards and Small Business Cards are not eligible for Card transfers in the U.S.) "
It sounds like they would transfer the card to the equivalent in the country that you are relocating to. So maybe a Delta Gold Skymiles, Blue Sky or simply a Blue. I don't know that they would necessarily change the credit card (revolver) to a charge card. I am pretty sure that Amex backdates in Canada but I cannot confirm this. But the most important thing is that you would have an older trade line reporting on your credit report in the US. Once you become established here you could always apply for the Amex that you really want; and it will be backdated on your credit report to your original Member Since date. So lets say you opened your Canadian Amex in 2001, you move to the USA and have the card converted to an American Amex that would report as opened 2001. Lets say in two years once your score has improved and you have American credit history, you could apply for the Amex Gold and it would be backdated and hence report to the bureaus as opened in 2001. Follow me?
As far as your second question, an annual income will be required for any card application here in the US, but very few banks have an income requirement to qualify for a card unlike in other countries. With our recent bank regulations called CARD Act, the banks/credit unions must ask for income. They take this amount and review your other obligations and enter the numbers into a formula. They must ensure that you are able to repay any amounts they may loan you. It is not a big deal really unless you are over extended.
If I may make another suggestion: Open a Nordstrom credit card. If you get down to Michigan you can apply in person or I believe you can apply online. Nordstrom is one of the few US companies that allows Canadians to apply for credit. You must pay in US funds so my suggestion would be just to make a few small purchases, get some cash at a US ATM and pay it at the store to keep it active. Then, once you move to the US you only change your address and BHAM! you have another US tradeline under your belt.
Best of luck.