As a programmer, I’d prefer a combination of the two: Dr Johnson kicked a large rock and said, as his foot rebounded, “I refute it thus.”. as I think it’s weird that a punctuation mark inside a quote can end the sentence that contains the quote. I’d argue like this: in the above case there are two sentences, the quote and the sentence that contains the quote. Both need to be terminated with a period.
A footnote in the article addresses this: "More logical still would be to have two periods, one marking the end of the quoted sentence and the other the end of the top-level sentence. But that would be redundant and also look ugly." I tend to agree with the author. While it's logically consistent, it's typographically redundant. There's no need to end a sentence with a full stop, a quotation mark, another full stop,…
Dr Johnson kicked a large rock and said, “I refute it thus.”, as his foot rebounded.
Is the period redundant? Or the comma after it? None of them? This looks almost as ugly as two periods.