Invasion of the leaf eaters

Japanese beetles have invaded my garden. This is the first year I've had them so I didn't start controlling them early enough. They are all over the hydrangeas and the cone flowers. Had to cut the rose mallow down it had been so badly chewed up. The wild rose was also in bad shape; I didn't cut it down completely but it got a pretty severe trimming. Unfortunately, I planted a rose of sharon tree a couple of years ago. I didn't realize it was an invasive at the time. It appears to be the biggest attractor. I'm seriously considering going back out and chopping it down but I'm afraid I'll disturb the roots of the adjacent peonies (transplants from my father's garden who got them from his father).