I don't know if you used Steam to Press your blocks, but, for me, steam distorts all my fabric and makes a mess of those wonderful straight edges I started with. They do look wonderfully flat, but what good is flat if they wave on the edges and the squares are no long square?
I do not use starch. I just try to handle the bias edges the least amount possible and I will run a staystitch 1/8" inside the edge of a long bias edge if the edges try to distort. Make sure the piece lays flat. If the piece cups up, then your stitches were too short or tight. Short bias edges don't really need the staystitch. Of course, this isn't going to help you after you have already stretched them.
When I have eased in fabric while sewing a garment, I have run a row of long running stitches and pulled the bobbin thread to make the piece shorter to ease it in. The extra fabric is eased in over several inches, not in just one clump. After the quilting is done, you won't ever see that tiny bit of excess.