Would this fit OS (31.8mm) bars?
Unfortunately no. Not unless you put it on the outer end of the bar where it's skinnier, but that certainly isn't ideal.
I have the twofish blocks and although they are a bit more expensive, they are truly handy. Fast and easy to put on/take off. Fit either size bars, and hold various size lights. Plus you can use them on your helmet if you want, very versatile.
I will eventually try one of the new mounts in the original post, just because. I would suggest using a piece of old inner tube around the bars first, so that maybe it won't have to be tightened so much and risk breaking. I use this method on all bar mounts anyway. Helps keep things in place.