Terry winds his like I do. I hold the shaft straight up and put 3 velcro strips on the lower shaft and start winding after the lock. Your first strap should be kind of close to the coil to prevent it moving in the water which will cause falsing. You can also use electrical tape. The reason to stand the shaft straight up as it will leave the correct amount of slack depending on your machine and coil size. Do not double your cable with sharp bends. It will cause the plastic sheath to possibly crack or the wires stress inside. Wash the wire with dish liquid often. 303 protectant is great stuff. Use it on the plastic box, the coil and the wire. It will help protect against UV damage. I am not a fan of silicone. There are some plastics that silicone will actually harm. Be careful with silicone, use 303 protectant. Google it.
EDIT: to add, I have never had any interference or loss of depth (that I know of) by winding the wire around the shaft on my Excal or any other machine. Most TV antenna installations tell you to do this to avoid interference. 300 OHM TV wire requires you to twist the flat wire along the entire installation. Wind the wire around the shaft is the correct way IMO. Besides, the wire is shielded just like a 75 OHM TV antenna wire, Sat TV or Cable TV. You don't need to wrap those or you can on an outdoor installation to be sure to eliminate interference. Running the wire straight along the shaft should have no advantage. Wrapping breaks up the pole on long cable runs. I used to install UHF/VHF antennas and we always wrapped the wire from the antenna down the pole. That was the correct installation.