I am doing the same thing basically. I don't know if I have a right answer for you but I was going to cover as much as I can and have it come bac k through. I need to figure out how to add soil and compost too. Weeds are thriving but the soil hasn't been taken care of for years and everything not weeds seems to be dying. The roots are at the surface. Its a mess. So I am doing that and then mulching and I have beautiful ground ivy. The only way I see to do it is to cover. But creeping thyme is more clustered together so not sure if that will work for you. Interested to hear responses as well. Good luck!