You do realize that we are talking about 200,000 sq miles of forests.
And they're planning to kill 450,000 barred owls over thirty years, according to the article. That works out to about 41 owls a day over that 200,000 square miles, or about one owl per 5,000 square miles per day.
Yeah, that'll make a huge difference. No way will the barred owls be able to overcome a reproductive disadvantage like that. /s