Low level ground cover

I am looking for some low growing ground cover which will grow amongst purple slate chippings around small paving slabs. I would say the ground receives decent levels of sunshine (middle of the day) with dappled shade as the sun moves round to the South West.
I had been considering Soleirolia soleirolii (Baby's tears) but have heard that these can be invasive and subsequently difficult to control. Hopefully this gives an idea of the height of ground cover I am looking for in a Tropical themed garden.
I am not avverse to using grasses (thinking "Hakonechloa macra" possibly)
dotted around either, so that is also an option.
Have included a photograph of part of the area I am considering doing this to.

 

Woolly thyme, definitely! Thymus praecox pseudolanuginosus. A lovely, gently-spreading aromatic plant with pretty lilac flowers. Doesn't mind being trodden on! Then there's Chamomile 'Treneague'..the non-flowering variety. Beautiful scent when brushed, but can be difficult to keep going for more than a couple of years.
Mentha requienii...very low growing but would need keeping in check.

 

Thank you, will give those a look, the Woolly thyme in particular sounds like it could fit the bill.