Misbehaving fabric certainly can take the fun out of sewing.
When faced with your dilemma, I match the top seam then sew two or three stitches. I leave the fabric under the presser foot then pin the bottom seam (to match). I gently tug the fabric while holding the bottom pin and sew. When I get to the pin, I remove it and use a stiletto to push the ends through. I usually have to trim the blocks or pieces to size because I tugged. I really dislike sewing a million little pieces together so....
When ever possible, I sew the WOF strips together FIRST then sub cut into the size I need; I Chain sew pieced pieces onto a WOF strip then sub cut whenever possible too. Sorry this won't help right now (unless you have extra yardage of your small strip stretchy fabric) for this project.