Hyphens, En Dashes, Em Dashes

Q. I’m proofreading a book that was previously published in the UK for forthcoming US publication. The hyphenation of “century” compounds using BCE/CE preceding a noun is inconsistent throughout. Examples: “A first-century-CE graffito from a wall in Pompeii”; “A second-century BCE satire.” My inclination, guided by CMOS 7.94 (on multiple hyphens), is to follow the second example, without a hyphen before BCE/CE, which is also how the UK edition was styled. I can’t seem to find any CMOS guidance that specifically addresses this issue, though. Is my inclination sound? Many thanks for any help.

A. We agree with your inclination, which also happens to be supported by Chicago’s recommendation to omit hyphens in compound modifiers consisting of a number plus an abbreviation, as in the 33 m distance (see CMOS 7.96, sec. 1, under “number + abbreviation”). That example isn’t perfectly analogous to a first-century CE graffito, but it’s close enough.

[This answer relies on the 18th edition of CMOS (2024) unless otherwise noted.]