The paper towel makes all the difference in the world. IIRC, the original Wayne method called for Viva! paper towels. before I found the Viva towels I tried Bounty and a few others. They would all leave lines as they weren't quite as thick or soft as the Viva brand. The Viva brand doesn't have "stitching" or embossments and is a very soft and thick towel. I would almost liken it to the blue shop towels on a roll you see at the stores, but even softer and thicker.
When I apply, I put some of the Enduro on the tip of the folded part of the towel. I then lay a bead of finish down the axis of the blank on the lathe and spin the lathe by hand all the while letting the towel "rest" on the blank. The spinning and very light pressure makes the towel act almost as a leveler for the finish instead of an applicator. In fact, I once tried a very thin plastic strip to level the finish, but found the plastic left me more lines. LOL