When I work with small pieces, starch is my best friend.
After you sew the first set together I would try to starch
the strip set before cutting them again into the 1 1/2 in pieces
that should set the fabric to hold it from stretching when
assembling them back together. If your seam allowance
is accurate then they should line up with no problem.
As mentioned when you sew smaller pieces your seam
allowance can make or break it. I as a rule always starch
my fabric before cutting any of the pieces out for the block
so the stretch is eliminated before I start sewing. Hope this
might be of some help to you.