New Foundations (NF), Quine's stratification-based alternative to ZF set theory, has resisted ordinal analysis for decades. While subsystems of second-order arithmetic and ZF have been assigned precise proof-theoretic ordinals via techniques like cut elimination and ordinal notations, NF and its variants remain largely uncharacterized in this sense. The recent direct proof of the Axiom of Infinity in NF-0 opens a door: if fragments of NF can be analyzed more directly, can one assign them meaningful proof-theoretic ordinals, and do those ordinals slot naturally into the hierarchy produced by iterated reflection principles such as beta-n-model reflection studied in the companion paper on dependent choice?