I think it's necessary to quilt the borders, at least as much as the main quilt. I have a way of quilting the border that I like, you mark spaces along the border, then straight lines between the marks to get a diamond type border. It's easy and I have gotten compliments on the border. Since you have square blocks, you could zig zag down one side, then the other, using the blocks for measurements. That is probably clear as mud, but I hope it helps.