Last year when I was paddling on Lake Diablo I met a guy that had built a small woodstrip canoe. He was using a kayak paddle that had a braided rope all the way around it as drip rings. I'm not sure what knot it was, but the ends of the braid were tucked into the knot so that you couldn't see the ends. It looked like one continuous braid. Sounds like this would be a good solution for you.

Maybe someone out there knows what knot it was.