So sorry I am not aware of any chemical weed killer that would kill weeds and not the creeping Jenny groundcover. There are broad leaf weed killers and pre emergent weed killers but these are not very practical in your situation. What I do with my thyme lawn is just choose a mild day, spread out a tarp, grab a bucket and get on my knees or belly and slowly remove any weeds by hand. I only need to do this once a year and I bring out some music and consider it my meditation. You do save time not mowing when you use a groundcover so put in a little time pulling the weeds - or just call the invaders wild flowers and enjoy a mix of plants as your blooming lawn. Keep growing, Marianne Binetti