A more practical and simple (and possibly legal) idea for abusing knowledge of irrational charity: Instead of asking for money to save countless children, ask for money to save one, specific child.

If one circulated a message on the internet saying that donations could save the life of a specific child, obviously if you then used the money for something unrelated there would be laws against that. But if you simply, say, A: lied about why they were in danger of dying, B: overstated the amount of money needed, C: left out the nationality of the child, and D: Used the money to save a large number of children, do you think a court would convict that?

Getting the money towards some cause where the child-saving is a lot less direct, like technological research or SIAI, would probably get hit for lying, but for something like fighting Malaria or the like that might be incredibly useful.