Not a diet, but a surefire cure for the little pests is DDT. It did the job exceptionally well and did not do any of the other absurd things it was accused of.
Bring back DDT and we can end the slaughter of upwards of 100 million people due to mosquito-borne illnesses since DDT was banned.
Everything I've read has said that DDT had a significant impact on the populations of raptors. Do you have any links to anything disproving that?
Or as an alternative, how about a logical explanation for why the population of bald eagles made such a significant comeback after DDT was banned?