I used the Binda/Cinelli's on a brakeless bike for almost a year. They held up, but barely. Those types of straps are not meant to be used on fixed gear, they are meant to be used on a road bike, where they will be subject to much less pulling force.
I recently switched to some toshi doubles, and the difference is night and day better. I can imagine that the toshi singles are also decent, but I would go with some doubles if you can afford it.