In other words, I define "morality" as "a system of 'shoulds' that humans can agree with".

If you want a name for your position on this (which, as far as I can tell, is very well put,) a suitable philosophical equivalent is Moral Contractualism, a la Thomas Scanlon in "What We Owe To Each Other." He defines certain kinds of acts as morally wrong thus:

An act is wrong if and only if any principle that permitted it would be one that could reasonably be rejected by people moved to find principles for the general regulation of behaviour that others, similarly motivated, could not reasonably reject.