Of course you can make a bargello without a pattern! Just draw it on graph paper. Draw the size/shape you want. Draw some (erasable!) lines to create the curves you want. Turn those lines into seam lines that are straight and divide the strips into individual pieces. Make a few copies of your drawing and start coloring. (I've always liked coloring in the lines - but still think outside the box.) Before you know it - you have a pattern. Don't forget seam allowances when you cut your fabric. You are ready to go.
I wondered how you were going to use 7 fabrics to recreate a pattern that only used three. You might want to add another couple of greens for your bargello so its introduction in the colorway isn't too abrupt. Just my thoughts.