My solution idea comes from the Bible, which tries to convince its readers that they should be kind to strangers in need, because they might be angels in disguise come to test their charity. (Paul said "be ye not fearful to entertain strangers, for some have entertained angels unawares".) What if concentrated charities funded "angels" to go around acting like they are in need of help, noting who helped them the most, and then giving those people large publicized rewards later, say in a couple of years? The help offered could range from giving directions to offering a job.
Those rewards, and the publicity that goes with them, might induce people to try to help folks they meet more often, so that they might win this "charity lottery". The percentage of administrative costs might be lowered by offering large rewards relative to the wages of the angel.
And this could be a "cased-based" rather than "rule-based" approach to charity; rather than setting up rules about who is worthy, the charity administration instead picks some prototypical cases they think should be helped. A donor who wanted to help someone like her when she needed help could just fund an angel to act a lot like she did then.
Might even make a good TV show, to promote the idea and make it vivid to those who might be rewarded by the angels. (Perhaps like the BBC TV series "Hearts of Gold" publicizing good deeds?)
As with all giving away of prizes, you really need to trust those with discression - the angels should be carefully selected and monitored. To avoid con-artists posing as angels, angels might publicize the fact that they never ask people to do certain things.
I understand that some people would be upset to learn they had helped an "imposter", and insulted at the suggestion they helped someone for the money. This is a problem.
As a variation, consider the the "Tell Off A Jerk" angel charity, which rewards folks for sticking their necks out in public and telling off some (perhaps big) rude person most folks would just try to stoically ignore. Imagine that candid camera footage ...