What is it to be called Kantian? Cool question but surely this can't be answered a priori. Kant's oeuvre is such a sprawling, hulking beast that to be called "Kantian" could mean all the things you listed, or just some. And then you have positions like Zizek's for whom the only way to to hew close to the spirit of Kant is to break with the letter:
"Let us take a great philosopher like Kant. There are two modes to repeat him. Either one sticks to his letter and further elaborates or changes his system, as neo-Kantians (up to Habermas and Luc Ferry) are doing, or one tries to regain the creative impulse that Kant himself betrayed in the actualization of his system (i.e., to connect to what was already “in Kant more than Kant himself,” more than his explicit system, its excessive core). ...One should bring this paradox to its conclusion. It is not only that one can remain really faithful to an author by way of betraying him (the actual letter of his thought); at a more radical level, the inverse statement holds even more, namely, one can only truly betray an author by way of repeating him, by way of remaining faithful to the core of his thought". (Zizek, Organs Without Bodies)
To speak soley for myself, the Kantian in me is defined by a few of Kant's innovations: his recognition that our epistemic relation to the world is no different to the epistemic relation to one's own self (I am as much a 'noumenon' as things 'out there'); his understanding that thought generates its own (transcendental) illusions, and that error is not just an 'empirical' problem; his conception of human nature as, effectively, 'second nature', a matter of enculturation that makes of human nature an ongoing process, rather than something 'given', once and for all. And of course his discovery and invention of the transcendental, as set off from the empirical, making time and space themselves not merely givens, but subject to a genesis of their own. Lots of very cool stuff that Kant did.