Some people use thyme between the stones in a path. I just posted a similar question in the herb forum asking if thyme would cover the rocks in a new part of my path. The rocks in my path are aobut 8-12 inches in diameter with about an inch in between. I was told by the herb folks that the thyme would cover my stones, but maybe your stones are larger and you don't mind them partially covered. I've been told that Elfin Thyme is the smallest.

I used moss between the stones on the part of my path I built a couple years ago. I don't think that will work on the new part because a lot of it is in full sun.

Here is a link that might be useful: New part of path

Could you try to kill the grass? I round-up my grass at the edge (I used the green metal edging). How bad is it? Whenever I see the grass start to come close, I go out with my clippers and clip them away. They dont get a chance. That also means doing them once every few days.