Steve's workflow in FCP will probably give you the best result for what you wish to achieve. Apply the Mask Shape Filter and adjust, then put the Mask Feather Filter on top and adjust (see PROJ 1 picture).
If you wish to add a very subtle blur to the edges of your projection you can do this in Motion. Duplicate your scaled image and put it on top of your original image. Apply a Gaussian blur to the original (bottom layer), so the image gest blurred outside its edges (can't do this in FCP). Then apply a mask to the duplicate image (top layer) and feather it until the masked image blends nicely with the blurred image (see PROJ 2 picture).
To Andy: I like your region blur filter. I will check out the others as well. Nice work!
Best wishes,
Ronny