As Robusto points out in comments beneath the question, there is no universally acknowledged rule governing whether to include or omit a comma after a conjunction at the beginning of a sentence. Robusto reports preferring to include such commas in academic documents, but many other writers and editors would not include them.
In my experience copyediting manuscripts for book publishers (including university presses) and later for magazine publishers, I don't recall ever having encountered a house style that required adding a comma after "And," "But," or the like. To the contrary, most house styles either said nothing at all on the subject or recommended omitting such commas, presumably for the reason that Words Into Type, third edition (1984) gives at the start of its long section on comma usage:
A comma should be used only if it makes the meaning clearer or enables the reader to grasp the relation of parts more quickly. Intruded commas are worse than omitted ones, but keep in mind at all times that the primary purpose of the comma is to prevent misreading.
The argument for including a comma after an opening conjunction is not, I think, grounded in a desire to make the meaning clearer (since the meaning tends to be quite clear without the comma, as Peter Shor indicates in a comment above), but rather in a desire to demarcate with exactitude the boundaries of the parenthetical expression that follows. Why Gregg Reference Manual would insist on such precision at the beginning of a sentence but not in the middle of one is a mystery to me.
There is nothing inherently wrong with using commas to break out parenthetical phrases regardless of where they appear in a sentence: It increases the number of commas in a work while (arguably) not making the sense of the text any clearer; but it's a style decision, and style decisions—if followed consistently—don't need to be justified.
On the other hand, if you don't want to add a comma after a conjunction at the start of a sentence, I don't think that you should consider yourself to be under any obligation to the preferences of Gregg Reference Manual unless your publisher has instructed you to obey it.
The three reference guidelines that you quote in your question evidently apply to any "parenthetical element," "introductory word, phrase, or clause," or "parenthetical or unnecessary expression" that immediately follows a coordinating conjunction—and the direct-address word "John" in your example is simply one such element, word, or expression.
That being the case, it seems to me that all three sources you cite would endorse omitting a comma immediately after the conjunction, yielding these sentences:
I was going to accept your resignation later, but John, have you considered all the options first?
I will be flying with the executive committee to London, and John, will you be coming with us?
The only asterisk attached to this endorsement is that Science and Technical Writing: A Manual of Style also approves of the alternative punctuation with a comma after the coordinating conjunction:
I was going to accept your resignation later, but, John, have you considered all the options first?
I will be flying with the executive committee to London, and, John, will you be coming with us?
So if you're following Dr. Darling or Morson, you should omit the comma after and or but; and if you're following Science & Technical Writing, you can choose either to omit the comma or to include it. I should note, however, that these three sources do not speak for more than themselves: there is no universally recognized rule of punctuation on this point.
Having said all that, I must reiterate Edwin Ashworth's suggestion that either preceding the conjunction with a semicolon or breaking the compound sentence into two sentences would do more to clarify the sense of the sentence on first reading than simply adopting one or the other approach to the comma question. Alternatively, in the first example, shifting "John" to a position immediately before the conjunction instead of immediately after it would enable you to punctuate the interior of the compound sentence entirely with commas, without fogging up the construction:
I was going to accept your resignation later, John, but have you considered all the options first?
In the second example, merely relocating "John" is less satisfactory because the choice of and as the coordinating conjunction becomes less appealing when "John" moves elsewhere. In that case, I would consider introducing an em-dash to indicate a redirection of thought midway through the compound sentence:
I will be flying with the executive committee to London—and will you be coming with us, John?
Best Answer
You ought to write it this way:
"The Disney version, generally considered both racist and sexist, portrayed the female characters in stereotypical roles and presented ethnically diverse characters with stereotypical features."
Comma before generally and after sexist. "Generally considered both racist and sexist" is a non-essential clause (it gives additional information about the Disney film).