Each of these concepts can be applied to our interest in presumptive equal custody on the basis of federal court decisions (though, technically, each is applicable only through dicta ... I say "technically" only because our question is the only family law question I can imagine that the federal courts haven't yet directly addressed). Each of these concepts is defeatable, however, unless it's tied to an antecedent concept: Fundamental Rights.
IF parenting (defined in federal caselaw as, [a parent's] "care, custody, control, companionship, and management" of his/her child) is a Fundamental Right, THEN, logically, it constitutes a premise for an argument as to whether any or all of the concepts above is the U.S. Constitution's specific way of protecting that Fundamental Right. Put differently, each of the concepts above is a weight-bearing column in an appropriately careful architecture of the structure of custody law; the Fundamental Right to parent one's own child is the bedrock upon which each column rests.
The hard skull work has already been done on all of this (both arguments of fact and law). There's no need to redo it. The arguments simply need to be tested in test cases. If you have an attorney with the reproductive organs necessary to go make the arguments, I'd be glad to talk with him/her about all the technicalities of it until s/he gets it. It's a makeable argument that simply needs to be made. None of us have any justification for anger at the system if we won't make the argument.
It goes without saying that the other workable approach to this subject is legislative. But that's not what your question was about.
Best of luck!