What a silly goose I am. Once an aircraft is reported, I just hit "c" for Crash Dive. Of course, I always "ride the vents" aka "deck's awash". IIRC, you have to set depth to 8 meters for "decks awash" or (I forget what the limit is in feet). It is a limitation of the vanilla game, the boat won't begin to submerge at less than 8 meters.
In the video you mention "Standard" speed and "decks awash", except your gauges show you are traveling at flank speed and are fully surfaced. You never went to "decks awash"? IIRC, I could dive a Gato/Balao in about 35 seconds with a standard crew, decks awash, at 11-13 knots.
Also, You list "hard to port or starboard" in the video, but never do this...Which is good, because you should not turn but dive straight down. Turning bleeds speed and should not be done.
See
http://www.history.navy.mil/library/online/ss-doc-2.htm
The video needs a good bit of cleaning up.