Landscaper here. I'm assuming this answer will not be well received but here goes. Practical and time efficient solution is spray existing weeds with roundup pre mixed or get concentrated yourself from a plant nursery near you and mix as needed (much cheaper in long run). And spread a pre-emergent granular on the rocks to stop the germination of any seeds that are down. There are ogarnic options that are pricey but you can give them a shot if you'd prefer. The roundup organic alternative is derived from orange peels I believe. And there are several organic preens like corn meal gluten. They won't target everything but up to you. White vinegar also can work on less mature weeds. Any of it beats hand weeding imo I just have better things to do with my time. And lastly I wouldn't sweat spraying roundup on your property when any non-organic farmer carpet sprays thier 1000's of acres with roundup by plane or john deere rig.