Citation, Documentation of Sources

Q. I am editing an article that includes the following citation:

Lactantii Firmiani, Epitome Divinarum Institutionum ad Pentadium Fratrem, ed. J. Davisius (Cantabrigia, 1718).

The author of the book is actually Lactantius Firmianus, and his book is entitled Epitome Divinarum Institutionum ad Pentadium Fratrem. But the edition cited is entitled Lactantii Firmiani Epitome Divinarum Institutionum ad Pentadium Fratrem. So should I change it to Lactantii Firmiani Epitome Divinarum Institutionum ad Pentadium Fratrem (all italics, no comma) and not put in the author’s undeclined name (although that might be confusing when text references have it undeclined)? Or should I change it to Lactantius Firmianus, Epitome Divinarum Institutionum ad Pentadium Fratrem (leaving Lactantii Firmiani out of the title, since it’s not part of the original title)? Or should I write Lactantius Firmianus, Lactantii Firmiani Epitome Divinarum Institutionum ad Pentadium Fratrem? Furthermore, should I cite the editor as J. Davisius (as printed in the book) or J. Davis (which was his real name)? Aaaarrrgh!!!!

A. It’s best to cite the information as it appears (presumably) on the book itself, as in your first version. If you feel the need to gloss any part of it (rarely necessary for classical authors and places), do so in square brackets:

[Lactantius Firmianus], Lactantii Firmiani, Epitome Divinarum Institutionum ad Pentadium Fratrem, ed. J. Davisius [J. Davis] (Cantabrigia [Cambridge], 1718).

[This answer relies on the 17th edition of CMOS (2017) unless otherwise noted.]