Re: Doubleswap theory. Why would Varys care if that were to be true? Not Aegon is still the Perfectly Prepared Prince, which is all that Varys wants, right?

I start from the premise that, if Varys could save Aegon, he would – for the same reasons that he attempted (but failed) to save Ned Stark and attempted (and succeeded) to save Gendry. 

Then the question is, what would Varys do with such a child? Well, from his dialogue with Kevan, Varys strongly emphasizes nurture over nature, that the problem with the Targaryens (although the analysis easily extends itself to Joffrey et al.) is that they are raised believing that rulership is their birthright, rather than their duty. Hence the idea that the monarchy could be perfected, and through it Westeros, if the education of the monarch is reformed. 

But as to why Varys might care about the second swap, I think it would be A. that someone he trusted betrayed him, and B. it would have involved the death of a child he would have gone some lengths to save.