To me, it seems to be purely personal preference. The semicolon between clauses suggests a connection between the sentences that is stronger than if there were a period between the two.
As (to me) it is generally acceptable to start sentences with the short conjunctions and and but, I believe the general rule can extend to independent clauses joined by a semicolon.
Possibly:
He is the most disagreeable person I've ever had the misfortune to meet, and I dislike his style; but I must admit that he gets the job done.
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
In this example, "as is Earth ... " is a subordinate clause. It is introduced by a subordinate conjunction, as. "Venus and Mars are planets" is an independent clause--it stands on its own. The fact that Earth is also a planet does not affect the truth or the meaning of that. Everything after the comma is, in effect, a "parenthetical" comment, and the comma here is correct. (Parentheses would also work, as would a dash--anything to separate the subordinate statement is OK.)