i think you could make this with tunisian. when it gets the the split, you could keep working half the stitches until both halves are long enough and then start stitching across the entire piece again at the other end.
The Staggered Eyelet stitch pattern produces a pretty all over eyelet pattern. The eyelets are produced by creating both a yarn over and a decrease. Working these two together creates the eyelet in the fabric and maintains the stitch count.