Thanks, BenB. Yes, the fethered shape mask does what I want. I tried it immediately after my original post, but failed to cancel the question before you replied to it.
I'll try to describe it better. It's similar to what happens when you put a cell phone's vertical video on a movie's horizontal frame. Without filling the empty space on either side, they end up black. Here I want to put a picture in the video frame underneath the overlay's frame, and blur the underneath completely. The boundary is where the overlay is visible and where the underneath frame is visible (ie., out from under the overlay). That shared boundary is where the visibility of one starts and the other stops. And it's that hardness of the boundary that I want to soften or blur.
Would that gaussian blur affect just one layer or both (background and overlay). I'll try to get to an example this evening. (The actual video I'm working with is personal.)