Dave,
I agree with you, having coiled line on pin rails and on the deck does make a difference between a well made model and a model that stands out. Don't get me wrong, a poorly built model ship does not magically become a masterpiece just because you coiled some lines for it. However, that being said, it is up to the modeler to make whatever decisions they want for their build and hopefully have fun building the dang thing.
I have a hunch that it's the line you are having issues with and not your coiling technique. Especially after the rigging you did for your amazing Chebec. I did an experiment with some line that was not Model Expo nor kit line.
Here is a series of photos to show you how I did this with a belaying pin rack, although it is really the same process I use with line coiled on the deck. I just set it up with the length being greater than the width. You might say that it is not a small coil but if you look at pictures of working ships, the length of the coil varies even on the same rail. If you want, I'll set up a smaller length on the pin rail. I hope this helps.
Steve
Here is the coil on the painter's tape already brushed with glue.
I use a straight safety razor blade to slip the coil off the tape.
Sorry this one is a bit blurry but this is the coil laid over the pin
And here is the coil brushed with water and just a bit of glue. I played with it a bit more so that it lay better.
Once that dries, you have a coil laid over the pin rail. As I said, to really make it look great, it needs to be moved around a bit.