What is the intent of your question? Maybe there are other interesting things out there you would find interesting -- topos theory comes to mind.
I know that someone (don't remember who) wrote a paper on directly axiomatizing the (super-large) 2-category of large categories, without reference to a formal set theory. Of course, his axioms provide for the construction of a large category Set, but I don't remember how that turns out to look. Maybe you'd find that interesting if you can find it?
Yes, I've been able to track down and purchase books on topos theory; including Mac Lane's Sheaves in Geometry and Logic and Goldblatt's Topoi; also, that article you referenced may be Colin McLarty's one on axiomatizing the category of categories; does this ring a bell?