I agree with Jan. Stitching in the ditch in the pieced blocks should not be difficult for a beginner. If the big stitch that Jan suggested is to hard, then just cross hatch the background without going thru the design. Many old applique quilts were crosshatched in the background. Good Luck. Your color selection was absolutely fabulous !!

I can't edit my original post, but wanted to point out that I was not suggesting using red & green thread. I would probably pick up the magenta that's in the batik before introducing another color, or else use one of the purple/violet colors so it blends in.
I tried to use black/white lines, but they didn't show up well, so I grabbed the first colors I thought would be most visible so you all could see the design. :)