On the recommendation of a kind commenter, I read an essay by Jonathan Schaffer called “On What Grounds What” (in Metametaphysics volume). Turns out reading straight up analytic prose is fun and edifying. Skipping large sections in the middle where Schaffer argues against Quine’s view that metaphysics (and ontology in particular) deals with the existence of things, the essay basically draws attention to the fact that the questions of existence are trivial – the really interesting question is not whether something exists, but how.
I conclude that contemporary metaphysics, insofar as it has been inspired by the Quinean task, has confused itself with trivialities. Hofweber 2005 speaks of ‘‘a puzzle about ontology,’’ namely how it could be that (i) metaphysics seems to ask deep and difficult questions, when (ii) the existence questions seem shallow and trivial. This is only a puzzle on the Quinean assumption that metaphysics is asking existence questions. The deep questions about numbers, properties, and parts (inter alia) are not whether there are such things, but how. [361-62]
So against Quine and Carnap, Schaffer proposes to do a bit of Aristotelian ontology. Why Aristotle? Not because it is cool or because it is another name that, in the name of some philosophical hipsterism, one can put forward and differentiate oneself from the herd. It’s Aristotle because he deals with issue of grounding rather than issues of existence, i.e. with the issues that are truly ontological and not trivial. Schaffer (easily) shows that most of the ontological debates aren’t about existence, but about what is more fundamental (prior, grounding, and so on) in existence, i.e. about the ordering of existing things.
I thus submit that a meta-metaphysics that would make sense of these central questions must make sense of claims of grounding. These central metaphysical questions are not questions about whether entities exist, but only about how they do. 
Basically Quine (and all other attempts at “flatness”) errs because his method presupposes ordering structure. The discussion then proceeds in an oddly non-continental way by asking questions not about who said what about what, but what sort of ontology would be better, flat or ordered. Better as a theory, not better for what.
Part of what makes a theory best (even by Quine’s own lights) is that it is a theory of what is fundamental (the ‘‘ultimate structure of reality’’). 
Some domains are metaphysically privileged. 
To conclude: metaphysics as I understand it is about what grounds what. It is about the structure of the world. It is about what is fundamental, and what derives from it. 
That last quote is the final sentence of the essay. So there is fundamental and there is derivative. I’m skipping of course the majority of the actual arguments. This is interesting on several levels, but mainly on the level of the counter-intuitive nature of “flat ontology” – it isn’t just that it cannot be consistently flat, but that the flatness, if it was possible, would contribute little to one’s metaphysical stance, doesn’t it?
And last and probably least: obviously privileging something over something is a form of ordering and therefore a form of “flatness” – but isn’t also the claim to explicitly not privilege something?