That sounds like a tricky site, because I’d have thought that most shallow-rooted plants would be liable to dry out from the established hedge taking all the moisture and from being sited in full sun. How about thyme? There are lots of varieties and it’s shallow-rooted. The low-growing (dare I say, “creeping”) types can even tolerate being trodden on, so the plastic sheeting and clippings wouldn’t be a problem. They also have attractive flowers. Or dwarf lavender? ‘Hidcote’ grows to about a foot. Other sun-loving herbs, such as oregano, could also work, but you’d have to choose a dwarf variety. I imagine they’d all need a bit of care (e.g. watering and even mulching, perhaps with gravel) in the early stages to get them established.