i had the same problem when i began quilting, till now i have now and then.
i solve it by washing the fabric, then tear it to a larger size of 3/4" then needed, starch it heavily,
cut to the right size.
sew with Angler 2 (from pam bono), in addition i put a note pad just lower then the needle so i am sure it is real the size.
even with those prevent actions, i get the block not all the time right, but near enough to the right size.
i dont iron the quilt when it is full top.
i sandwich the top following sharon schamber method. keeping it strait.
do not quilt it too heavily, but all the quilt the same quantity of quilting (it is make a huge change, and distortion! if you quilt heavily/non heavily on the same quilt).
then when i bind it, i cut the binding stip from the length of the fabric, as well heavy starched. - i got a tip from some one, if i pull it a little while sawing, it keeps the quilt strait. it works.
good luck!
becky