As a writer or editor, how many times have you heard “The main thing is to be consistent”? When it comes to hyphenating, capitalizing, italicizing, and other style choices, the best way to carry through on consistency is to keep a style sheet.
There is a part of CMOS 7.75 that continues to trouble readers, probably because it is an exception to the general rule (stated at 6.9) that “periods and commas precede closing quotation marks, whether double or single.”
“The full names of administrative bodies are capitalized. Adjectives derived from them are usually lowercased, as are many of the generic names for such bodies when used alone . . .