At first I thought your issue is as Tartan described and to a certain extent that is what caused it but it is the nature of the pattern so I don't see how you could have avoided it as you were working on it with so much bias and so many "slap and sew" borders with the way the quilt is assembled you couldn't attach those pieces any other way. The fact that there were so many compounded the issue at the edges. About the only thing that could have prevented that issue from happening was to heavily starch all your fabrics, and I mean stiff as cardstock starching, before starting to reduce the amount they could stretch.
So the only way you can resolve this issue now is to put in some darts and then quilt over them as much as possible to camoflauge them. They really aren't super noticeable once completed. I am thinking, if possible you may be better off putting in several smaller ones rather than one or two large ones.
I was faced with the same issue on a hand pieced client quilt several years ago. Here is a link to pictures I posted of the quilt. If you scroll down to the 5th picture where I posted a close up of the border you can see one of the tucks I had to take at the bottom of that pic. There is another tuck in that same picture closer to the top (near the burgundy diamond) and it is barely noticeable. In fact the only reason you can spot the one near the bottom of the pic is because it is a close up shot.
Hand pieced quilt quilted by Feline Fanatic
And yes, I informed the client of the issue before doing the tucks or darts.
Edited to add, it really is a very pretty quilt!