Folks - I planted pink lemonade thyme here in NYC a few years ago since a family member has allergies to grass. We've been manually weeding all along but life has gotten far busier with kids and we need a tool to speed up the process. I'm thinking a certain kind of mower would do it but a lot of the weed is 8-10 inches high up from the ground (please see pics). What would you recommend I can use once a week? Manual weeding 30 mins every day is just impossible nowadays with kids at home all the time

Thanks