I have this bag attached to a Surly LHT with Nitto Randonneur bars. It continually wants to rotate downward, with the bag falling back onto the headbadge of the bike. This picture shows the bag as I'd like it to sit:




The U-bolt idea might just work, as it does have a hard plastic back/lining to it. I suppose a downside to doing that would be that it would end up sitting a little high on the bars and wouldn't allow me to use the top of the bars while riding (at least it would partially block the bars).

I can try to get some pictures later today, but hopefully you get the idea.