I suspect the way they are sprung is based on holding the string as it would be found on a right handed instrument.
When I needed a capo, I didn't want to screw something into a vintage banjo neck. I made one using a bent (pointed end) paper clip hooked over the string, heavy nylon fishing line tied so it runs under the strings and down under the neck where it is attached (stitched through) to velcro. At the other end of the paper clip, a short piece of clothing elastic for tension and the other end of the velcro, to fasten the whole thing firmly. The combination of velcro and elastic allows it to fasten firmly at different widths of neck when capoing higher or lower.
Where the back of the paper clip might dig into the sid of the banjo neck, I wraped and stitched an offcut of vinyl fabric which I had used to make a banjo carrying case following the "sling" design in Pete Seeger's How to play 5-string banjo book.
The design has worked well for over 20 years. I ave replaced fishing line and nylon a couple of times.
Quack!
GtD.