You are assuming a rule that I believe is a pseudo-rule (perhaps you could quote this 'rule' from some grammar?) I'd personally have no trouble with
Tom went to France and Dick went to Belgium.
It's clear enough. The addition of a comma before and would not worry me either - I'd add a pause if reading that version.
Here is an endorsement of the optional dropping of that prescriptive comma:
When a coordinating conjunction connects two independent clauses, it
is often (but not always) accompanied by a comma:
Ulysses wants to play for UConn, but he has had trouble meeting the
academic requirements.
When the two independent clauses connected by a
coordinating conjunction are nicely balanced or brief, many writers
will omit the comma:
Ulysses has a great jump shot but he isn't quick on his feet.
( http://grammar.ccc.commnet.edu/grammar/conjunctions.htm )
What disturbs me far more is the rambling and over-punctuated nature of the example sentence. Two at least are needed - the garden-path flavour of the original might even lead some to misconstrue it, being led to believe that ' the subject of the two independent clauses is the same'.
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
The usage you have shown is incorrect.
Anything parenthetical, i.e. anything that can be optionally dropped, needs to be surrounded by commas. In this case there should be a comma after the "and" in order to surround "as a result". British and American comma usage can vary but this is one thing these two cultures are united on.