How can I do this? Blur overlay, or something?

I've got three layers of video: Background, picture-in-picture, and a border around the PIP video. Three video layers and two composites. So far, so good.

Problem: Now I want to add a title-clip over top of the video, and blur what's behind the title.

If I just blur all three layers individually it doesn't do what I want: There's still a sharp border where the PIP is overlayed on the "main" video. This is also a PITA as I'd have to fade the blur in/out in all three layers (keeping them in sync with each other).

I want to have everything behind the text (title-clip, on "top" of the other video layers) blur smoothly.

Any ideas?

Thanks...