You may need to remove the offending areas of plasterboard, including areas
around as well, and reboard putting polythene between the board and the
battens. It would appear that the salt has worked its way through the
battens, but a layer of polythene should stop it from happening again. I
know you don't want to take it all off, but I presume its not happening over
all the wall is it? Very often the most severe course of action is the one
that will last.