I would use fusible applique to make the center. Cut a piece of fabric the size of the center (it should be the color you want for the top background) and then layer the other pieces on top of that. You can print the pieces from EQ and then trace them onto fusible or directly on the fabric. Just make sure to remember to reverse where appropriate.
Does that make sense? I don't think trying to piece it will be very much fun, and it's all about fun, right?