I have the same situation with a new walkway under a pergola...what a mess after rain,ugh!
I'm putting in creeping thymes(dug out sand/gravel and transplanted with compost-soil)
There is a plant called Irish Moss, Stepables has it on their web site. This might be good in your zone. Check out their website,it is a good one.

yes try a steppable. corsican mint might do it for you. also
consider some of the other mints and/or thymes. bloom periods are relatively short and a run over with the mower will keep them shortand non-blooming. Check for rcommendations with herb growers.
diggerb

It's probably too late by now but we used Blue Creeper between our flagstones. I've been very satisfied with it. Tiny blue flowers are pretty too.

I have had corsican mint in between flagstones that get morning sun for years.
It smells awesome, but unfortunately after several years, the moss took over!
It does spread really well and lots of it has shown up in other areas of the yard where I never planted it! We have found Blue Star Creeper to be SO invasive!
Do not plant it where it can enter your lawn! It covers everything in sight! Moss will not take full sun, it will dry up and die. Creeping thyme is a nice choice as
well as the corsican mint. I think anything will start to grow over the stones. Just get some pruners and prune them.