I'm not sure if 36x36 would work. Assuming I'm doing my math right, each area on the map (a square each with its own island) would be about 5 inches sqaure. And based on a low-quality picture I did find of the map (that only shows the islands, not the entire map itself), each island would have to fit in an area that's about 1 inch square (if I were to make each island to scale). To me, that'd be next to impossible to applique 1 inch islands (or less with any small islands around it) and I'd loose a lot of detail (a LOT of detail).
Sue, I think you found the perfect fabric. But I'm not sure I want to pay almost 4 dollars a yard for it. Got anything a little bit cheaper? Oh, thanks for the info on the applique, Barb. :)