Thanks again to all of you for responding! Most of the patterns suggested fall into the same (beautiful) category: sew strip sets, cut to square, line up and sew around the edges, cut into diagonal quarters, re-sew, spend hours arranging and finding new secondary patterns. Hidden Wells, Summer in the Park, and the Three Dudes are like this. They look fascinating, and endlessly amusing (I feel your pain Laura! Hard to settle on just one arrangement!)
Also, there seems to be consensus that I will not face a disasterous outcome if I mix my (prewashed) stash fabric with the (unwashed) pre-cuts. I have been following the wash-or-not-to-wash discussions on other threads on the board since I joined a couple of months ago, and it seems as though everyone has very good reasons for doing it the way they do it! My reasons are mostly selfish - I like the extra fabric handling I get to do when I wash, line dry, iron and fold my new fabrics away. I did have one occasion where the fabric disintegrated along invisible flaw lines after washing, so at least in that case pre-washing saved me some grief! (But mostly I do it for the tactile pleasure.)
Since we are just talking, and no one is going to hold me to any of this (right?) I am sort of thinking of trying a bargello, but putting a little convergence applique on it, or maybe three...Just talking...*takes deep breath to calm racing heart*...not saying I'm actually going to do this...just a thought...