Ha-ha--digging up and resetting the rocks is not in my personal universe either (which is why I keep battling that one area in futility
--maybe someday I will expand my universe or let it go)
My antennaria gets afternoon shade from about 3pm on. Supposedly, they need full sun and obviously mine advances over the rocks just fine with afternoon shade. You could try it in the shady spot--nothin' to lose really. I'm sure it would do well on the sunny sidewalk. Those parts in the pictures above going across the rocks just lift up--like a tight carpet--the stems are all intertwined and have little roots hanging but they aren't even attached to the rocks. It's pretty amazing stuff.