Hi, Boyd. I think that you could use one good tile to cast a fiberglass female mold of your exact tile and then make a male mold from that. You could then use the two molds to press new material into exactly the configuration that you need. However, this will be very expensive. You might check your local area to see if there are any prototype shops that could do this work and get a rough idea as to what this would cost you. My guess is that it would be big bucks.
A better approach might be to check the house restoration magazines like Family Handyman and Old House Journal for ads from the companies that make the tin cieling tiles and pick a tile close to the original and replace the whole ceiling. They also have the edge tiles, which you would probably have to duplicate also.
There are products that can be used to fill holes in metal but they all have to have some section thickness. This would include things like filled epoxies (Bondo) and fiberglass. Since your tiles have to fit against the ceiling, I do not think that they would be of any use to you.