I don't have any SHB here yet, thank the good Lord.
What about water with a few drops of dish washing soap like Dawn? Breaks the surface tension of the water so even the small light weight bugs fall through and drown. I use is to kill Japanese beetles. They drop like lead sinkers. Well, not that fast, but they drop. :) Like I said, I've never had to deal with the little devils, so don't know if it would work on SHB or not.