How can I unambiguously differentiate between the absence or presence of a period in a quote?

For example, take the following sentence that refers to a text message:

This happened after she told me "Okay."

If the original contents of the message did include a period, it would serve a double purpose. However, if it did not, one must be added. This means that there are two equally valid interpretations of what the actual message was. It could either be "Okay" or "Okay."

I believe that the latter has a colder and more rigid tone to it, and therefore I would like to clearly convey that the exact contents of a given text message either contains a period or does not – without changing the structure of my sentence. How can I do so?

One option is to italicize the word okay:

This happened after she told me okay.

This type of italicization is known as "using the word as a word."

If you followed British punctuation conventions, it would be clear from the outset whether the period was included in the original quoted expression, because British conventions call for putting the end-of-sentence punctuation outside the close quotation mark if the original word or phrase quoted did not end in that punctuation mark:

This happened after she told me 'Okay'.

and for putting it inside the close quotation mark if it was included in the original wording:

This happened after she told me 'Okay.'

The Oxford Guide to Style (2002) provides a fairly detailed discussion of what it calls "British practice" in section 5.13.2 ("Relative placing [of quotation marks] with other punctuation"):

Except where the matter is quoted for semantic or bibliographic scrutiny, the relationship in British practice between quotation marks and other marks of punctuation is according to the sense. While the rules are somewhat lengthy to state in full, the common-sense approach is to do nothing that changes the meaning of the quotation or renders it confusing to read.

In US practice, commas and full points are set inside the closing quotation mark regardless of whether they are part of the quoted material. The resulting ambiguity can cause editorial problems when using material from US sources in British works.

When the punctuation mark is not part of the quoted material, as in the case of single words and phrases, place it outside the closing quotation mark. Usually, only one mark of of terminal punctuation is needed. When the the quoted matter is a complete sentence or question, its terminal punctuation falls within the closing quotation mark, and is not duplicated by another mark outside the quotation mark: [examples omitted].

The only exception that Oxford identifies to the rule of not using more than one mark of terminal punctuation is "when the terminal punctuation of the quoted material and that of the main sentence serve different different functions of equal strength or importance," as in

Did he really shout 'Stop thief!'?

Unfortunately, U.S. punctuation conventions (generally speaking) are insensitive to this nuance, prescribing the same punctuation in either case:

This happened after she told me "Okay."

This isn't the case (as Oxford implies) across all U.S. disciplines; I recall from my law school days that the Harvard Blue Book was quite punctilious about putting end punctuation within the close quotation mark if it appeared there in the original content being quoted and outside if not. But for the most part, U.S. punctuation conventions are as Oxford describes them. The Chicago Manual of Style, sixteenth edition (2010) offer this comment on U.S. practice:

6.9 Periods and commas in relation to closing quotation marks. Periods an commas precede closing quotation marks, whether double or single. ... This is a traditional style, in use well before the first edition of this manual (1906). ...

In an alternative system, sometimes called British style (a described in The Oxford Style Manual; see bibliog. 1.1), single quotation marks are used, and only those punctuation points that appeared in the original material should be included within the quotation marks.

The Associated Press Stylebook (2007) extends the punctuation convention prescribed by Chicago to U.S. journalistic practice:

PLACEMENT [of quotation marks] WITH OTHER PUNCTUATION: Follow these long-established printers' rules:

—The period and the comma always go within the quotation marks.

—The dash, the semicolon, the question mark and the exclamation point go within the quotation marks when they apply to the quote matter only. They go outside when they apply to the whole sentence.

So, under the predominant the U.S. punctuation convention, writers can't easily achieve the clarity and precision available to their British counterparts. Instead, they must to live with ambiguity in these situations—or have to try to execute an end run with something like the italics maneuver noted above. Or reword to move the quotation way from the end of the sentence.