First of all, while it's true that there are many different styles, there is still definitely a "British punctuation" versus an "American punctuation" at a generic level. What you have flagged as "American" is almost always used throughout North America without exception(*). And while there is more variation in Great Britain, what you have given as "British" is still widely used there.
(*) In North America, some style guides do allow for a mix of "British" and "American". For example, The Chicago Manual of Style (6.9) says that the British style (using single quotation marks) “may be appropriate in works of textual criticism or in computer coding and other technical or scientific settings.” This is necessary when text styling is unavailable, and putting a punctuation character inside quotation marks could lead to confusion with text that is meant to be communicated literally: (1) Type the password "123." versus (2) Type the password '123'.
Aside from search and replace on the quotation marks themselves, an editing tool called PerfectIt will let you choose if you want final punctuation inside or outside of quotes. Unfortunately (and ironically), it's not perfect when it comes to the British style; but I can't see how it could be. Short of artificial intelligence, software can't tell if what's inside quotation marks is actually part of quoted dialog or just a quoted "fragment" of text. And the British style does put punctuation inside of quotation marks if it's part of a sentence's broader grammatical structure.
- 'The pears,' he said, "apples and other fruit have all dried out.'
- The pears, apples and other fruit have all dried out.
The comma is part of the spoken sentence here, so it does come before the quotation mark---even in the so-called British style. (As does the period.) Adding quotation marks and narrative text doesn't change the punctuation of the quoted dialog itself. (Note: As most, but not all, British style guides avoid using a serial comma, I left it out.)
However, PerfectIt will flag such instances and let you decide if they should be fixed or not.
As much as the (common) British style makes more logical sense to me (even though I don't normally use it), the American style is easier from a programming point of view.
But while you can find tools that let you get close to automatic styling, there is really no substitute for learning the particulars. (If you rely on any automated tool, it will let you down at some point as far as this is concerned.)