Federal Aviation Administration Accountability Enhancement Act This bill addresses provisions related to whistleblower complaints of misconduct by managers within the Federal Aviation Administration (FAA). Among other provisions, the bill renames the Aviation Safety Whistleblower Investigation Office as the Office of Accountability and Whistleblower Protection (OAWP); requires the OAWP to investigate whistleblower complaints that it receives or that are referred to it concerning misconduct by managers or a violation of any other provision of federal law relating to aviation safety, and make recommendations for any disciplinary action arising from such investigations; creates an Office of the Whistleblower Ombudsman within the FAA to educate employees about whistleblower rights and prohibitions on retaliation, and serve as an independent resource for agency employees to discuss their rights and remedies for any allegations of misconduct; establishes an Office of Professional Responsibility within the FAA that receives and assesses any complaints of misconduct by managers within the FAA; directs the FAA to establish a policy that governs misconduct investigations according to best practices to ensure independent and objective investigations; and sets forth a discipline management policy that governs adjudication of misconduct investigations.