I  know that OpenSSH knows an "escape character". For example, you can
  terminate the session using "~.", even if the remote host  has  frozen
  and won't let you log out using the normal "^D".

  Well,  but  sometimes  this  doesn't  work.  I had no idea why until I
  finally had a closer look at the friendly manual:

   The escape character is only recognized at the beginning of a line.

  Aha! You have to hit return before entering "~.".  In  actuality,  the
  "escape character" is an "escape sequence": "\n~", not just "~".