Key Democratic operatives and private investigators who tried to derail Donald Trump’s campaign by claiming he was a tool of the Kremlin have rebooted their operation since his election with a multimillion-dollar stealth campaign to persuade major media outlets and lawmakers that the president should be impeached. The effort has successfully placed a series of questionable stories alleging secret back channels and meetings between Trump associates and Russian spies, while influencing related investigations and reports from Congress. The operation’s nerve center is a Washington-based nonprofit called The Democracy Integrity Project, or TDIP. Among other activities, it pumps out daily “research”...