In Fallen London, death will not release you — even if you die.
Racking up too much Scandal, Suspicion, Wounds, or Nightmares will ship you off to a Place Of Menace: the Tomb-Colonies, New Newgate Prison, a river-crossing ride with the Boatman, or the Royal Bethlehem Hotel/Mirror-Marches, respectively.
I was surprised to see this forum post, which suggests that the place of Wounds is the easiest to escape and Wounds itself is the easiest Menace to manage; this runs directly counter to my experience. (The post references Hesperidian Cider, which has more details in this auction.) I've found that Wounds is either expensive or inconvenient to reduce, that most Wound-reduction actions only take off a single point of Wounds, and that the Boatman's ride is time-consuming to escape.
So, I ask: without spending Fate/Nex, which place of Menace is the easiest to escape, and what's the trick of it? Which place is the hardest to escape, and what limits your ability to leave quickly? (Please mention all four places of Menace in your answer.)