My own answer to the question, at least off-the-cuff, is that the best thing I can think of would be a way to restore rez immunity. If someone rezzes into the Orange Badness and pops Second Wind or Lucid Dreaming or any other 'I need to recover' skill, they are now doomed to die as things currently stand (unless Rescued). Being able to replace the rez immunity on someone in that situation would let a healer keep them alive even without having Rescue.

So the change I would make is basically having an 'Immunized' status be visible after rez, and having it change on action to 'Immunizable' (with the same remaining timer as Immunized had), and giving healers an oCGD cast which turns the 'Immunizable' status back to 'Immunized' (again, keeping the current remaining time the same).

That'd address a huge portion of my own Rescue use; in the other scenarios, there's now nothing a healer can really do any longer... but a death—or even a wipe—are not the end of the world.