Punctuation before ending a quotation

(Changing the word order just complicates the issue.)

For a long time, due to potential problems with damage to lead type, the convention was to typeset punctuation inside quotation marks where they would be protected.

Today though, that reason no longer applies, and quotation marks should contain what is quoted and punctuation should go where it belongs. (Many "traditionalists" would disagree, but their tradition is historically recent.)

For this sentence, I would punctuate it:

“Much wow, Bercow hid his opposition to Brexit so very well when he was Speaker.”, Mark Wallace, executive editor of ConservativeHome, tweeted.

That is, the period is part of the quotation, the comma is part of the overall sentence.

It wouldn't be wrong though to omit the period.

But putting both a period and a comma inside the quotation marks is just wrong.

UPDATE:

Ont the other hand, sometimes the "inside" rule might be worth retaining, if only for its comic effects.

E.g. the same rule was applied to parentheses in later editions of the King James Bible, producing what we would consider to be a smiley face:

Exodus 32:25 And when Moses saw that the people were naked; (for Aaron had made them naked unto their shame among their enemies:)

For a complete list, see Words In Parentheses, and search for ":)" to highlight this specific case.