1) Update the cart area so that once something has been added, a clearly visible checkout button shows up within the box.
2) When a user clicks to checkout they should be taken to a page that requests a first name, last name and email to start the checkout process (this way, we as site owners can collect their details for future marketing)
3) Show them a page saying "Hi NAME, we like to ensure our customers shopping experience is as safe and easy as possible. As such we process all our orders via amazon. Please click below to continue placing your order" obviously followed by a nice checkout with amazon button
Cheers,
David