The relevant rule in Chicago is rule 3 in section 8.167 of Chicago Manual of Style, Fifteenth Edition (2003):
8.167 Headline style. ... (3) Lowercase prepositions, regardless of length, except when they are stressed (through in A River Runs Through It), are used adverbially or adjectivally (up in Look Up, down in Turn Down, on in The On Button, etc.), are used as conjunctions (before in Look Before You Leap, etc.), or are part of a Latin expression used adjectivally or adverbially (De Facto, In Vitro, etc.)
[Relevant example:] Taking Down Names, Spelling Them Out, and Typing Them Up
Chicago acknowledges that this and its other five rules for handling title-case headlines are arbitrary. It calls its rules "pragmatic rather than logically rigorous but generally accepted"—presumably meaning generally accepted by publishers who pick and choose among Chicago's style recommendations in assembling their own house style.
In any event, the out in the headline "This Is How He Finally Got the Hell Out of Mexico!" is functioning in the same way as the out in Chicago's example, "Taking Down Names, Spelling Them Out, and Typing Them Up": It forms a phrasal verb (in one case with "Get"; in the other with "Spell") with a verb that is separated from it by one or more intervening words (in one case "the Hell"; in the other "Them").
That the final phrase "of Mexico" is irrelevant to the status of out as part of "Get Out" is clear if you remove "the Hell" from the equation—which is a legitimate shortening of the title because the person in in the title isn't removing the Hell from Mexico, but rather his own person. In that simplified case, Chicago clearly prescribes this punctuation:
This Is How He Finally Got Out of Mexico!"
The only situation where Chicago would endorse lowercasing the o in out is if the word were functioning strictly as a preposition, as (arguably) here:
This Is How He Finally Got His Burro out of Mexico!
I am confident that Chicago would recommend this capitalization of the OP's title:
This Is How He Finally Got the Hell Out of Mexico!
It is One-Sided
The rules you quoted from the Chicago Manual of Style essentially tell you to capitalize everything except:
- "articles, prepositions, coordinating conjunctions (and, but, for, or, nor) or such modifiers as flat or sharp following musical key symbols"
- compound words where "the first element is merely a prefix or combining form that could not stand by itself as a word"
- "the second element in a hyphenated spelled-out number"
"Sided" is not an article, preposition, etc. "One" is not a prefix that could not stand by itself, because it is a word. Finally, "One-Sided" is not a spelled-out number.
In addition, you can find a few papers on Google Scholar that confirm this usage:
Best Answer
"The Gulf" is usually capitalized, because it's functioning as a short form of the name "the Gulf of Mexico" rather than as an ordinary use of the common noun gulf. (Of course, the Gulf of Mexico is a gulf, so it's not wrong to write "the gulf" in a context where you've just referred to it. But it's also an "ocean basin", so an easy test is: in any given occurrence of "the gulf", could you happily write "the ocean basin" instead? If not, then it's because you're using "the Gulf" as a short name, and should capitalize it.)