If you really wanted it down on the bars you might be able to use just the top half and put a piece of foam under the top half and then use a small zip tie or better yet come kind of cleaner looking wire arrangement of some sort to cinch it down and affix it to the bars.
I was just thinking you could connect to the two screw holes that are in the top half of the unit. I hope you can figure out something that looks halfway clean, those road bars are quite wide aren't they? The unit fits around my MTB bars with the 31.8 stem size no problem.