I strongly suspect that what is left is not an irreducible "object" in the common sense, but rather that the part about how these atoms behave the way they do is all that is left after a fully complete reduction. No object-style "atom", only the behavior. The behavior is the atom.
Does that help?
Basically, the way I understand it, you don't reduce to quarks and leptons, and then wonder "But how oh how do these quarks do this and that? Why do they do it?". Instead, you reduce to the wave function, and there is no quark left, and nothing left to explain; the behavior of the quark explains both our perception of the presence of some "object", and the interactions / rules / physical laws.
The behavior is the atom.
So, suppose you finally added that elusive last term in the equations of the Theory of Everything, and there is nothing to the Universe but "the behavior". You press "Run" and the computers running your model produce a beautiful multiverse out of nothing. Where are the computers and who pressed "Run" to create the universe we live in?
If it's worth saying, but not worth its own post, even in Discussion, it goes here.