The puckers could be from a triangle or block edge that is not on/ or on a bias...I can never remember which...
But I do know that the long edge of triangles can stretch, that may be the reason for the puckers...
It looks like a very complex, advanced quilt. Where did you find the pattern?
Also, when pressing blocks or seams, if you use steam it can distort the blocks. I have been told to use starch to keep them "squared"
Hope this helps.
Also, could you do a very quick, light, cold water wash to get the fibers of the material to line up again so that you might be able to quilt it without a lot of "easing"? Just a thought.
Kirsten