I haven't started a string quilt or even a scrappy (paper bag) type quilt for all of your above reasons. I've spent a bit too much time on quilts where I've used coordinating fabrics with instructions that say to 'place blocks in a pleasing arrangement' - can't imagine how I'd go about a total random string/scrappy! And I, too, love the look of other's that certainly appear random.
Maybe the simple answer is to just 'go with it' and see whattcha get?
Yes, a picture would be wonderful
Good luck!