I have the mediums and they fit my size 10 winter boots as well as my partner's women's size 9 running shoes (well sort of, they were a bit loose). So the size range is pretty large. You are solidly in the size large, so I would probably go with that first. The benefit of the smaller size is that they will fit tighter, but the downside is that they may compress across the tops of your toes more. On my lighter hiking boots, that was fairly noticeably and may be bothersome if you were running. To eliminate any slack in the chain on the larger size, you may need to pull the back up a bit higher, but this is easy to do and don't think it will slip much or at all once you do that.
Here are some pics I posted of fitting them on my various shoeware:
Even in the pic that shows the chain hanging off the bottom of her shoe, I was able to pull up the back to pretty much take up that slack (and I don't think you will get anything like that, even though your light hikers are going to be much smaller than a winter boot).