Warren,
ETSY recently changed their rules that allow you to drop ship to your ETSY customer, so now you could get the order from ETSY and fill it from FAA.
The only real challenge you will have is that it is not possible to offer different types of product in a single ETSY listing. For example, with ETSY you can list different prices for different sized photos, but you cannot list different prices for metal, canvas, acrylic, etc. In that case you would have to list a Canvas version of your image, another listing for a metal version of the image, etc. Each listing can have multiple prices for multiple sizes.
Hope that helps.
Dave