Ok - here's the scoop, at least for me. Using ifunbox, I moved the files into the "shared folders" area, just like itunes does. Again, starting esword HD simply deletes them.
I then skipped that part, and loaded the files directly into the esword HD area - i.e. where the kjv.bbli files already are. Boom - it all works.
So, something isn't working right (for me) when I put them into the file sharing area, but ifunbox let me put them directly to the right place - so yay!