We have woodpecker issues where I am as well and they're illegal to shoot. One of my customers bought a device that does exactly what you were asking. It picks up motion and plays the calls of predatory birds. Solved their problem in less than a week.

The fake owls and stuff worked for a couple days before the woodpeckers realized they were fake.

[Link: urbannaturestore.ca]

Not exactly what they got but the idea is the same