Before I start sewing I tie a double knot about 3 inches from the end of the string. That way, when you are done sewing you can tie the two ends together on the same side instead of wrapping anything. As far as getting the needle through, I do it just a few at a time. It takes a little more work but well worth it. Sewn korkers are definately toddler proof (believe me I have a crazy one!) There's nothing worse than someone spending their money on something that can easily be pulled apart.
Keep sewin' those korkers