I think most moss can tolerate light foot traffic. Yes, you can use roundup to kill the weeds. Roundup doesn't hurt moss.

You're probably best off finding the moss that's growing wild in your area in similar environments to your stepping stones. Read some of the FAQs posted on this forum on moss propagation, they're full of excellent information.

Zinia ,I have scraped sections of moss from different areas of my yard ( it doesn't seem to grow that deep )and along with it about a quarter to half an inch of underlying soil and placed them between my stepping stones. I would then stomp on the moss to get it to ,sort of adhere to the ground underneath. I have even run my wheelbarrow loaded with wood over the areas and so far so good.Even if some of it dies, there should be enough to propagate more. I dont know what type we have here in pennsylvania ,or whether its the same you have in N.C...I too got tired of grass growing between the stones and hopefully the moss will choke out most of any grass trying to fill in the same area. And best of all no trimming is required....Tom in PA.

Thank you for the good information. I've been noticing moss in parts of the yard I haven't noticed before. Will encourage some to grow in other places as well as the stepping stones.
zinia