I mean the equivalence / transference proofs. Otherwise you're pulling a theorem out of the air and telling students to just accept it. And by "accessible" I mean easy enough to understand that they don't become a huge distraction (or worse).
Our use of R rather than star-R is merely a quirk of history - we managed to justify R to ourselves first, hence it's the "standard".
(If you look at the other axioms, the hardest one to justify is the bounding axiom, and its necessity is reinforced by proof. Every other axiom fits in with the student's understanding of arithmetic.)