I watched Run Silent Run Deep the other day and looked carefully at the shots of the sub diving. I know that's probably not the most scientific way to come to a correct value, but it did seem that SH4 was fairly close to the mark, if perhaps a little slow.
Needless to say, getting a fast dive time is one of the central themes of that movie, so you could always try doing what one crewmember suggests - leave the hatches open
They do take a while to get under, but that's hardly surprising when you consider that they were massive in comparison to a Type VII U-Boat, roundabout double the tonnage in fact.
Look on the bright side; imagine how long an I-400 would take to dive, that thing was 400 feet long, with 177 crew on board.