That's a hard one, Linnea. I have big rock slabs in a straight-ish path. I've been experimenting for three seasons and there are a few challenges. One is nothing gets going early enough so the ground is just bare at least until mid-June. Second, even when I've put good soil between the stones, the drainage isn't great. I don't want to introduce stone dust because then the weeds are even harder to get out.. Same problem as yours with ajuga. Tried 3 different thymes and they come back very weak. or not at all. I've tried a lot of steppables including the ones that say they withstand automobile traffic ( kidding) Foot traffic and they do not. Sedum does not hold up to foot traffic.

Mazus repans should have worked but I see no signs of it. Last summer I finally bought cheap six packs of portaluca (sp...moss rose) and they lived and flowered. I see teeny tiny seedlings now, but it is already June.and if they get to blooming size it won't be until August. So I'm planting the edges with flowing perennials, moss roses in the spaces.

A friend of mine created a strict geometic pattern with stones like yours and planted that little ground cover "Platt's Black" It was stunning. I tried that plant and it also died.

I pretty sure you'll find something that works. I think I hijacked your post, but there's a lot of plant angst going on in my garden.

a low Geranium sanguineum could work, there is a Nanum-cultivar, I think

hardy

semi-shade to full sun,

tolerates to be steped on to a certain degree

spreads by rhizomes, so "occupies its spot" in the long run,

I have several G sanguineum-cultivars, (z7, good loam, dry summer)

rhey are resilient and hardly reseed for me