If you want to try bleaching again, try using a resist to keep the bleach out of places you don't want it..I'd try a sample first to make sure it will work. A really cheap resist is gel school glue...the blue glue in a bottle...and it's washable. put the glue onto the fabric you want to protect....should only need a solid line of it along the edge...let it dry, then use the bleach pen on the part you want to clean up. Of course, after you're done you need to wash it again to get the gel glue out.
Depending on the design of the wall hanging, you might also want to try doing what our local quilt shop owner did on one where her fabric ran..she added more color and added quilting around the edges and make it all part of the design. Hers looks great!