I know this will be tough but you have to do this. Go to your local fabric shop and purchase what is called sizing. This is the material that is used to create a hem on a dress or a pant leg.....strange enough it looks a lot like bar tape. And I am sure it come in myriad of colors.
It comes to mind that I thought somebody on CR maybe a year ago was talking about this same subject. They added one more twist once you have applied the the new tape apply some varish to give it that old weathered look. (Dale was I correct on this) : -)
See if that works.
Get back to me.
Jack (Giacomo) Gabus
Laguna Beach, CA