Sheilajoyce, that tablecloth will become a treasured family heirloom. I'm sorry I have no advice about securing the ends. The weaving in method you described sounds good to me. Are you worried about it coming out? I wonder if you could secure with a tiny dot of that clear stuff that stops frays. (Used to be called Fray Check, but comes in a tube and has another name now.) Don't know whether you'd want to do something like that to your masterpiece or not!!

Sheila, for what it is worth, here is my advice: Because you have put so much time and work into this project, you will definitely not want those ends to come undone. It is not going to make an unsightly lump to make a bit of a knot with just one loop around your needle. I would weave into the cloth, away from the edge for about an inch, then make the one loop knot. I would then weave in the same direction as before, for another inch. Then I would double back, but not exactly in the same place as before- move up just a bit (this way you'll avoid making a lump in the piece). If you choose not to use the one-loop knot, I think you should add one extra thread-through in the opposite direction.

In my opinion, it also helps if you do not use a blunt yarn needle, but a sharp one which will enable you to split the thread when you weave in, not just through the easy spots in the stitches between threads. It will hold faster that way.