Hi, Ian and welcome to permies.
We have both green and brown stinkbugs. The damage they do here is mainly to the surface of my tomatoes...sometimes making the skin so blemished it is inedible. The best method I have found for them is a shake of each plant while keeping an eye on what drops. During the summer I sometimes get one per plant (and I squish them). I do this every day that I can. It is harder to find them with mulch but I found that the stinkbugs
land on their back and play dead for a bit...their bottom side is kind of greenish yellow. When I find them elsewhere I just pick and squish...here, anyway, they seem to show up as singles instead of hoards like blister beetles or squash bugs.
I am anxious to hear other suggestions.
"We're all just walking each other home." -Ram Dass
"Be a lamp, or a lifeboat, or a ladder."-Rumi
"It's all one song!" -Neil Young