So when you have a single quote mark followed by a double, that doesn’t change where the period goes. It goes inside all the quote marks. Apostrophes are different.

Turning off the quotation mark formatting will prevent all future quote marks from changing, but it will not undo those already written in a document. To override existing marks, simply delete ...

I figured that, yes, commas are needed. After all, there’s a rule that says quotations are set off from the rest of a sentence with commas. But that rule doesn’t apply in every situation.