Would the swifer sheets work ? (Don't know never used ) ?
Good, strong colonies seem to help the most. I have used the sheets in the past. In a colony or two, the bees didn't read the directions. Instead of tearing them up, they propolized them down. That allowed hiding places for the SHB. After seeing that, I have gravitated back to beetle jails or beetle blasters. The only problem I have with those is forgetting to remove them prior to tilting the top brood box for inspection. That makes a really bad mess and you loose some bees that way.
My opinion is, whatever you use, keep it up. Constant trapping, observing bee space, full sun, beetle jails, SHB sheets, etc. be vigilant about it.
Tilled garden soil and compost piles are nice soft, convenient locations for SHB to complete it's life cycle. Those locations are everywhere. It is possible, if there aren't any existing honey bee colonies in the area, that it may take a year or two for SHB to locate your colonies.