Looking for methodological diversity is more of a PSI thing. There's already a ton of grad students doing qualitative work - but it's ultimately about who applies and who accepts, right? PGSC looks more for regional interest in applicants, like what part of the world you're interested in studying. The divide between the two divisions is pretty substantial - PGSC is heavily theoretical and usually attracts people who intellectually work in Marxist tradition. PSI tends to be more about (domestic) public policy and policy-related issues like family, educational inequality, etc. The department is pretty small, so you have to be sure you know what you want to study. But there's also a lot of opportunities to collaborate with other departments like public health, education, etc.
And yep - rumor has it they're looking for 6 people this year, as opposed to the normal 4. But the new funding system (which is pretty hefty - same as other private elites) still applies to the new cohort. Hope this helps!