I'm no expert on this but I can share w/you what I know.
Woodpeckers LOVE to peck at cedar siding shingles. If that's what you have for siding, you could be in for a looong haul. Now, you need to determine WHY they're pecking on the house. (You need to become a Woody Woodpecker!) If you're looking for a mate, pecking at ANYTHING (to 'drum' up a sound) is one reason why. Or, maybe 'lunch' is in there (behind the siding or something, depending on the part of the house that's getting drummed.) Beyond those 2 reasons, I don't know of any other reason they'd peck. If it's mating season, I think you're hosed. If it's for feeding, well, find out what kind of food is 'behind' the siding and start spraying.
OK, moving right along ... You may be able to 'distract' the Woodys by putting a feeder somewhere between the location of the house and the nearest tree (of their liking.) Once they discover it, gradually move the feeder further and further away from the house until you can 'tolerate' the drumming. Then, slowly but slowly stop filling the feeder, and he may, perhaps, go away. It's also possible he may begin a search for food and end up RIGHT back at your house! It's a game ya know so vary your patterns because they DO learn them.
Other than trapping them (which you can do) or doing as you suggested, I haven't much else to offer.
My best to ya and hope this helps.
Jay J -Moderator
PS: Visit a library or bookstore or Pet Store and find a good book about Woodpeckers. Again, if you want to know how to BEAT them, be one!