I'd focus on the software side of 'real' problems and team up with others project focusing on the engineering side. Still keep to my core area I know best while still tending towards these kind of real worldwide problems.

I'd also love to fund research that misses out because it can't be monetized easily.

With money to burn you could certainly make great strides in improving software in many areas of the sciences. A lot of tools used daily in areas of biology for example are very capable but were typically designed for use by the original author only. You could improve the lives of countless grad students and other researchers simply by providing a decent UI and good documentation. The savings and benefits would be enormous but you certainly would not make any money doing so.

I assume you're being ironic? I think the jury's out on both of those things being real problems.

Correct, with the only qualifier being that this only applies to juries that are composed of anti-reason, science illiterate individuals.