About half-way through last year, I swapped from regular screened bottom boards to screen bottom boards with an oil tray for SHB and mites. The SHBs hadn't been bad when I was checking regularly last summer and fall, but when I looked the other day, it had been since around November, so there were more, but they had more time. I will say that the SHB will fall into the tray. They work as advertised.
I am hopeful that they will help with the SHB. I'm hoping a full year will supply a better idea of how well they work.
It is my opinion that the SHB will become more of a threat to bees than mites eventually.