String blocks are one of my 'go to' blocks for mindless sewing. I don't sew onto paper though, it goes straight onto squares of batting (stitch and flip). The batting is often (usually! :D) pieced left overs from squaring up something else, as are many of the strings. I keep a separate bag of triangles in the string box so nothing is wasted.

The squares of batting are cut 1/4" bigger than the finished size to allow for squaring up. If you cut the sashing at 1", this brings the blocks together (edges of batting touching) if 1/4" seams are used. Only the backing is needed now to finish a quick quilt for Linus. I have seen these blocks sewn together without sashing, the seams have to be pressed pretty heavily though.

I make these blocks as the mood takes me and keep them until I have enough that I think will go together to make a quilt.