Passenger trains along the Gulf Coast are inching closer to reality as Amtrak secured critical funding Monday for improvements needed to restore service, nearly two decades after Hurricane Katrina flooded the region’s rail infrastructure. The Transportation Department awarded Amtrak a $178.4 million grant for required track and signal work, crossing upgrades and station improvements before the line can take passengers from New Orleans and Mobile, Ala., which could be as early as next year.