Answer for Japanese Beetles
I try everything every year and last year found the answer: 'Bug Stop' by Spectricide. I had it on hand to kill a huge invasion of Asian Lady Beetles that were coming into the house and decided to try it on the Rose of Sharon and the Perennial Hibiscus (which the J. beetles absolutely love). It got rid of them for the rest of the summer!
I also have a Paw Paw tree that they decimate each summer and it worked on that too.