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luminosity comments on On Charities and Linear Utility - Less Wrong
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Your entire point seems to be that it's better to give to multiple charities when the joint utility of giving to those charities exceeds the benefit of giving all the money to one charity.
This circumstance exists in the real world for most individuals so infrequently as to be properly ignored. It is extremely unlikely that there is some combination of charities such that giving $5,000 to each of them will generate substantially better returns than giving $10,000 to the best available charity. Unless I'm ignoring important evidence, charities just don't work together that comprehensively, and non-huge sums of money do not have dramatic enough effects that it would be efficient to split them up.
Also, you chose an incredibly dense and inefficient way to make what seems like a very simple point.
Off the top of my head, one charity might be worse overall but might need a small amount of funding to attempt an experimental strategy aimed at improving it. If the likelihood of finding a better way than the most efficient charity pursues is high enough, then small funding to the experimental charity and the rest of your donation to the other could be optimal.
In general I am uneasy with suggestions that one should focus all their charitable energy in one direction, because people are far too prone to finding a local maximum then ceasing exploration for higher maximums.
If this were true, that would mean that that charity had extremely high but rapidly diminishing marginal returns, in which case you should give it money until those diminishing MRs brought it below your next best option. I'm pretty confident that diverse investment is only proper where charities exhibit interactive returns (which is probably extremely rare for most people's value of charitable contributions) or whether you are trying to maximize something other than effective charity.