Ordinarily parenthesis should be marked with commas on both sides. But Fowler recommends that the first comma should be left out after a coordinating conjunction if what follows is a simple adverbial phrase—if I interpret him correctly. (Coordinating conjunctions are and, or, but, and possibly some semi-conjunctive adverbs like so, therefore, however, etc.) The comma should be retained before a subordinate clause or when its omission would cause ambiguity. This probably includes conjunctions that are not at the beginning of a sentence. Fowler's advice seems balanced and practical.
Cleopatra appeared poised and composed. But on the inside, she was seething with rage. — Simple adverbial phrase at the beginning of a sentence.
Her only option was to support Mark Anthony once again. But, if he should perish, it would be the end of her. — Not a simple adverbial phrase but a clause.
She knew her cause was lost and, in a fit of final despair, had a serpent brought in to extinguish her life with its venom. — Not at the beginning of a sentence.
The relevant text from Fowler's The King's English follows. He is arguing for general laxity with adverbial phrases, and would generally allow both commas and no commas around them. He goes on to say that, if commas are used, one must never omit one but write the other; however, he gives the above rule as an exception, in order to avoid an abundance of commas, logical though they might be.
Laxity once introduced, however, has to be carefully kept within bounds. It may be first laid down absolutely that when an adverbial clause is to be stopped, but incompletely stopped, the omitted stop must always be the one at the beginning, and never the one at the end. Transgression of this is quite intolerable; we shall give several instances at the end of the section to impress the fact. But it is also true that even the omission of the beginning comma looks more and more slovenly the further we get from the type of our above cited sentence. The quotations immediately following are arranged from the less to the more slovenly.
His health gave way, and at the age of fifty-six, he died prematurely in harness at Quetta.—Times.
If mankind was in the condition of believing nothing, and without a bias in any particular direction, was merely on the look-out for some legitimate creed, it would not, I conceive, be possible...—Balfour.
The party then, consisted of a man and his wife, of his mother-in-law and his sister.—F. M. Crawford.
These men in their honorary capacity, already have sufficient work to perform.—Guernsey Evening Press.
It will be observed that in the sentence from Mr. Balfour the chief objection to omitting the comma between and and without is that we are taken off on a false scent, it being natural at first to suppose that we are to supply was again; this can only happen when we are in the middle of a sentence, and not at the beginning as in the pattern Cranmer sentence.
Any expectation of a comma in the examples of the OP has very little to do with the subordinate clauses' restrictiveness, but rather, as the OP suggested, with an interruption of their natural flow. When leading a sentence with a subordinate clause, the comma does not force a "parenthetical / non-restrictive" interpretation. Simply, compare the meaning of two sentences:
- If you work hard, you get rewarded.
- You get rewarded if you work hard.
None of the embedded phrases in the examples were relative clauses, so the concern of imposing a non-restrictive interpretation is irrelevant. In every case, the embedding did put the interrupting phrases in a parenthetical position--even if they are considered "essential" to the meaning of the sentences.
The reference to section 6.32 of The Chicago Manual of Style 16th edition established a legitimate exception to a general rule of commas. If omitting an appropriate comma creates no ambiguity, omitting it becomes a matter of style opinion rather than grammar. Moreover, if we believe an appropriate comma introduces ambiguity, our best solution is to recast the sentence to remove ambiguity.
Considering the options for each example:
1) This is the country where[,] if you work hard, you get rewarded.
(relative clause)
The relative clause is where you get rewarded, and the comma is appropriate, because the embedded conditional phrase, if you work hard, interrupts the natural flow of the clause. The conflict between the locative where and the conditional if might be manageable enough, but many would be more comfortable with the extra comma. If the sentence had been written: This is the country where you get rewarded if you work hard, certainly no commas would be needed.
2) We need to talk because[,] if we don't, we will be in trouble.
(adverbial clause)
The adverbial clause is because we will be in trouble, and the comma is appropriate, because the embedded conditional phrase, if we don't, interrupts the natural flow of the clause. With such minuscule conflict between because and if, there is very little risk of confusion in omitting the comma. If the sentence had been written: We need to talk because we will be in trouble if we don't, certainly no commas would be needed.
3) London is where[,] when I was young, I used to live. (noun clause)
The predicative is where I used to live, and the comma would be appropriate, because the embedded adverbial phrase, when I was young, interrupts the natural flow of the clause. The locative where and the temporal when are nearly irreconcilable and should probably be separated by a comma. If the sentence had been written: London is where I used to live when I was young, certainly no commas would be needed.
4) Give me a call if[,] when you are at the station, it rains.
(adverbial clause)
The conditional clause is if it rains, and the comma is appropriate, because the embedded adverbial phrase, when you are at the station, interrupts the natural flow of the clause. The conditional if and the temporal when seem to be in deep conflict and would work better with a comma between them. If the sentence had been written: Give me a call if it rains when you are at the station, certainly no commas would be needed. The slight ambiguity could easily be eliminated by recasting the sentence to communicate the true intentions of the imperative.
5) It is useful when[,] if it rains, you have an umbrella. (awkward
adverbial clause)
The awkward adverbial clause is when you have an umbrella, and the comma is appropriate, because the embedded conditional phrase, if it rains, interrupts the natural flow of the clause. This construction is awkward with or without the comma, but would probably be less confusing with the extra comma. If the sentence had been written: It is useful when you have an umbrella if it rains, certainly no commas would be needed. The overall awkwardness still suggest a need to recast the sentence.
6) She is the person who[,] if she is faced with difficulties, can
handle them very well. (relative clause)
The relative clause is who can handle them very well, and the comma is appropriate, because the embedded conditional phrase, if she is faced with difficulties, interrupts the natural flow of the clause. The conflict between the relative who and the conditional if might be manageable without a comma, but many would find it less confusing to see the comma. If the sentence had been written: She is the person who can handle difficulties very well if she is faced with them, certainly no commas would be needed.
7) He said that[,] if all goes well, he will call. (noun clause)
The noun clause is that he will call, and the comma is appropriate, because the embedded conditional phrase, if all goes well, interrupts the natural flow of the clause. The conditional in the context of reported speech is the least awkward of the seven examples and fits the exception of The Chicago Manual of Style perfectly. If the sentence had been written: He said that he will call if all goes well, certainly no commas would be needed.
Conclusion:
The ultimate purpose of commas is clarity. Use one if it makes things more clear. Leave it out if it makes things less clear, and in my humble opinion: when in doubt, leave it out. Most importantly, recasting the way we put phrases together can eliminate most of our comma confusion.
Best Answer
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:
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:
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:
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: