Thank you, Luis and Karsten. To answer your question, Luis, I'd been trying to add the simple border via, well, the Simple Border effect. That works fine for PIPs that don't need to be trimmed, and for photos that aren't getting a Ken Burns effect. Otherwise, not so fine.
Before I saw Karsten's reply, in desperation I'd already done a somewhat kludgy approach, along the lines of what Luis suggested: I put a generated rectangle behind the PIP, and carefully sized it to spill under the PIP just enough to look like a border, with the PIP stacked atop the rectangle in the story line.
The key, I found, was to make those 2 into a compound clip. Until I did that, the dissolve never looked right: there was a glimpse of the rectangle (not just its outer edges) behind the PIP, on both the dissolve in and dissolve out. But when the dissolve was applied to the compound clip rather than to the individual components, everything worked.
But my, that was more tedious than I'd have liked. Next time, I'll use Steve Martin's plugin.
Thanks again for the help,
Rich