In the 13 years since he suffered a string of political setbacks and quit the third most powerful job in Washington, Newt Gingrich has been busily laying the foundation for a comeback to an even grander perch. On any given day, the former Speaker of the House can be found on a chartered jet headed to Iowa to train future GOP candidates through his American Solutions group, or in Phoenix discussing ways to lower health-care costs with drug makers through his for-profit Center for Health Transformation. He might also be in Philadelphia, narrating a film produced by Gingrich Productions, or...