LA RUE, Ohio—Doug Hafer recently spent a few hours picking up softball-size rocks from a field with one of his daughters. He trimmed the bushes at his house, changed a fan motor on the refrigerator after his wife complained it was making a noise, and plans to put a new button on the front doorbell.

Like many farmers across the Midwest facing an exceptionally rainy planting season, Mr. Hafer is looking to fill the days he would normally spend planting.

He...