That could be viewed as self-employment which is prohibited and regarding how you get paid, you should contact a U.S. tax accountant because my understanding is that you still would be subject to the payment of U.S. taxes.
So, despite the fact that the company would be a Canadian entity, I would be considered self-employed. Would a simple workaround be enough to thwart this, such as having a friend own the business, and proceed to hire me as a remote employee?
The only real obstruction I'm worried about is the legality of doing that work for money. I have some friends who I could employ too, and lots of cash could just sit with the company, but if I can't work for that entity (legally) there's no point in starting it.