I had a similar problem with the Bethlehem Star. Those diamonds are so tricky because of the diagonals. They tend to stretch when you sew them. I am not sure what I will do with my Bethlehem Star. It will be my last UFO to try to conquer.
I do have a couple of thoughts for you though. First, make a full size template of one of the large diamonds, maybe use freezer paper and see if you can use steam and get them all back in place where they belong, then starch them real good before piecing. Those bias edges may be willing to go back in place.
If not, how about making it look like a broken star by putting some strips of the background in between them. Maybe even do something off the wall with them. Lay each one of them out on a big background square and applique bias tape around them. Your diamonds are pretty. I would definitely try to use them somehow.
Because of my experience with diamonds, I will never do it again. Just make this one a converstion piece and enjoy it.