Going forward or going forwards?

Does using quotation marks exonerate one from using correct punctuation within the quote?

It should be either: "I think we should adopt this approach, going forward" or "I think we should adopt this approach, going forwards" or perhaps better still, "Going forward, I think we should adopt this approach".

Another Americanism which irritates me is "Theresa May declared a general election Tuesday" rather than "Theresa May declared a general election on Tuesday".