Higher fencing is the way to go. I find it does help that my chickens have other areas of their own, though. They like loose sand or peat moss to dust bathe in, as well as loose dirt. There are a lot of things planted for my chickens to forage on, in addition to the grass. Clovers, alfalfa, native plants, chard, kale, berries, etc. Some protection while getting started is important. They also love to scratch around foraging in leaf litter. There are always little life forms for them to eat under any type of mulch pile. If the mulch isn't deep or chunky, mine usually don't fling it everywhere. They can get to what they need with just a little light scratching, it doesn't require major digging. A spot where you can turn over a shovel full of dirt will keep them busy foraging, too. Maybe you can give them a little corner with some alternative activities, until you get your fence remodeled.
