Did you put any wood chips on top of the plastic pathways or gravel?
My sister-in-law has a major garden every year and sells her produce at the outdoor farmers market on each Saturday during the summer. She has her produce sectioned up in wooden or cinder block areas. And she starts all of it in early spring while there is still frost at night indoors on the enclosed back porch under grow lights. So her produce is safe from the creepy crawlies while it's getting started.
Hanging trays might work. I can think of a multitude of ways of rigging it up. I still think the aquaponic systems are best for next to no weeds and keeping the creepy crawlies away. Even the PVC pipes with holes drilled into them and the water running trough can work.. along with using water with fish poop for the fertilizer. using water. I saw some systems some kids had made for their science fair project that worked well. The big systems had the long water grow beds with something like styrofoam sheets laid out on top with holes for the small grow baskets pushed in. They used coconut husking for the filler in the basket to grow the seeds.
https://www.youtube.com/watch?v=F-tiSc7G53Q
Cheapest Hydroponic System For Everyone | Under $1/100 Rs
You might like this system.
Having studied numerous types of systems, love aquaponics best.
https://www.youtube.com/watch?v=M10_nBVP7SU