Well, I won the battle with the tulle but my attempt definitely has room for improvement. The tulle was a little annoying to work with. It would not gather with the sewing machine no matter how I adjusted the tension and stitch length. After sewing a line of stitches along the length of the tulle strips, I had to hand gather it before attaching them to the skirt. This took much longer than I thought it would.
After sewing on a couple of the strips, I had a look at the skirts on the sites I got the idea from (shown here and here). It appears that they were much more generous when gathering the tulle than I was. On my next attempt I'll be sure to be more generous. Click on the picture for a closer look.