After lots of detective work, recording the 55-minute loop with my mobile phone in my pocket, playing it back on my PC, using the Shazam app and Spotify, I have the updated playlist. All tracks are easily found on Spotify.com using the information given. Timings are based on the Spotify app media player for Windows PC.
DHS Main Entrance Area Music, Updated Summer 2016
Sahara: Main Title - Charles Gerhardt (from Classic Film Scores: Casablanca), 01:44 to 02:28
King Kong - Charles Gerhardt (from Classic Film Scores: Now, Voyager), 03:00 to 07:18
Aliens: Futile Escape - James Horner (from Titanic And Other Film Scores Of James Horner), 00:00 to 02:10
Main Titles - James Sedares and The Phoenix Symphony (from Elmer Bernstein: The Magnificent Seven/Hallelujah Trail by The Phoenix Symphony), 00:00 to 02:05
The Death Hunt (From "On Dangerous Ground") - Bernard Herrmann, Charles Gerhardt (from Classic Film Scores: Citizen Kane), 00:00 to 02:23
Snow Picture (From "Citizen Kane") - Bernard Herrmann, Charles Gerhardt (from Classic Film Scores: Citizen Kane), 02:50 to 3:17
The Sea (From "Beneath the 12-Mile Reef") - Bernard Herrmann, Charles Gerhardt (from Classic Film Scores: Citizen Kane), 00:00 to 01:56
The Octopus; Homecoming (From "Beneath the 12-Mile Reef") - Bernard Herrmann, Charles Gerhardt (from Classic Film Scores: Citizen Kane), 01:20 to 03:55
The Abyss - Alan Silvestri (from Voyages, The Film Music Journeys of Alan Silvestri, 01:30 to 02:45
Victory At Sea - Richard Rogers (from Ebb Tide/The New Limelight by Frank Chacksfield & His Orchestra), 00:00 to 06:55
The Sea Hawk (Suite) - Charles Gerhardt (from Classic Film Scores: Captain Blood), 04:55 to 06:36
Talking Drums; Prelude: The Riverboat; Petticoat Dance; The Safari (From "White Witch Doctor") - Bernard Herrmann, Charles Gerhardt (from Classic Film Scores: Citizen Kane), 00:00 to 03:58
Overture - Bernard Herrmann (from The 7th Voyage of Sinbad), 00:00 to 01:55
Escape To The Clouds - Bernard Herrmann (from Mysterious Island - Original Film Soundtrack), 00:00 to 02:12
End Credits - John Williams (from Indiana Jones and the Temple of Doom (Original Motion Picture Soundtrack), 00:00 to 03:10
The Bride of Frankenstein - The Tower Explodes And Finale - Kenneth Alwyn & Franz Waxman, (from Bride of Frankenstein by Westminster Philharmonic Orchestra), 01:08 to 01:48
The Bride of Frankenstein - The Creation - Kenneth Alwyn & Franz Waxman, (from Bride of Frankenstein by Westminster Philharmonic Orchestra), 5:58 to 7:45
Opening: Let There Be Light - John Williams (from Close Encounters Of The Third Kind), 00:00 to 00:40
The Visitors / Bye / End Titles: The Special Edition - John Williams, (from Close Encounters Of The Third Kind), 07:18 to 08:00 (not precisely what is on the DHS loop; placeholder until I find the exact one)
Main Title - James Horner (from Star Trek II: The Wrath of Khan Original Motion Picture Soundtrack), 00:17 to 02:40
Willow (Willow's Theme) - James Horner (from Ron Howard - Passions & Achievements), 00:00 to 03:27
The Adventures of Robin Hood: Main Title / Coronation Procession - Erich Wolfgang Korngold (this track is not the exact one, merely close to it; it is a placeholder until I can find the correct one.) section lasts 03:15