Glue baste the joins instead of pinning the joins. I do this at the ironing board. Align the seams as you want them, then put the tiniest dot of glue inside the seamline and press with the hot iron. I use Elmer's washable white glue. The glue washes out later or, if you need to open up the seam, comes apart if moistened with a drop of water from your fingertip.
Note: It is still a good idea to pin an inch or so before each seam. You can take the pins out as you get to them so you don't sew over them. This helps ensure that you don't have excess fabric on top or bottom when you get to the glue-basted seam.