Canvas clipping with "feather" edges effect

Question

I'm currently drawing an image to an HTML5 Canvas and masking it with an arc, calling clip() before I draw the image so that only the portion that's in the arc is shown. How can I feather the edges of this arc? I know from googling around that there is no simple way to simply apply a "feather" to a shape drawn with canvas. What abut going in on the pixel data for the image where its edges touch the arc? Thanks for any help.

Here is the relevant portion of my code:

ctx.arc(canvas.width/2, canvas.height/2, 250, 0, 6.28, false);//draw the circle
ctx.restore();
ctx.save();
ctx.drawImage(background, 0, 0,
              background.width * scale, background.height * scale);
ctx.clip();//call the clip method so the next render is clipped in last path
ctx.drawImage(img, 0, 0,
              img.width * scale, img.height * scale);
ctx.closePath();
ctx.restore();

UPDATE

Thanks for the thorough answer and very helpful code/comments Ken!! I spent a few hours last night trying to work this solution in my particular use case and I'm having trouble. It seems that if I clip an image with the second-canvas technique you describe I can't redraw it on transforms the same way that I can with an arc() and clip() routine. Here's a JS Fiddle of what I'm trying to accomplis, minus the feathering on the arc, notice the click and drag events on the two layered images.

http://jsfiddle.net/g3WkN/

I tried replacing the arc() with your method, but I'm having a hard time getting that to be responsive to the transforms that happen on mouse events.