Rather they act so as to best be seen as caring, kind, helpful, rich, etc. I am pretty sure that there are ways of working on capturing their donations - and putting them to better use.

I can't see many ways of doing this besides changing the social atmosphere, such that people who donate to ineffective charities aren't seen as doing as much good as people donating to effective charities.

Perhaps the place to start in shaping public opinion is with people who don't donate. They have little to gain either way, so might be more willing to change their perceptions. Moreover, many contrarians will jump on board just for the sake of being able to devalue the status quo. Once non-donaters have been publicly convinced (and they are a large majority in the total population) then charitable people will be forced to change their donation strategies in order to maintain status.