Sounds like Seminole piecing or a variation of it. I've never tried blocking a strip set but I think Barnbum did it with her flower bargello and it worked for her.
One word of caution with this border. Once all assembled you will be attaching I bias edge and your quilt will have a bias edge. I recommend loads of pins when attaching to keep it from stretching on you and a stay stitch on the outside edge to keep it in shape for quilting. Sounds lovely, can't wait to see a picture.