This sounds crazy but I'd add even MORE puckers in the background during pressing (if possible) and then sew over them to create a "textured" background. You could fuse the whole thing onto a fusible fleece to "preserve" the existing texture too. If you've ever taken a close look at some of the pieces shown in the international quilt exhibitions, you've seen examples of this technique -- backgrounds that are purposely "bunched up" to add interest and dimensionality.