In "The New International Version," your information is totally wrong. I looked up most of the meanings of the words that supposedly meant something else than what was originally said and you totally twisted everything up! Here is an obvious example, toward the end, was written:
"Notice the subtle change from the idea that a believer should not perish to the idea that a believer shall not perish. Should indicates that the believer has no excuse in perishing. Shall indicates that a believer cannot perish."
"shall" does not indicate that a believer cannot perish. This is the definition of "shall"...
plan to, intend to, or expect to: I shall go later.
will have to, is determined to, or definitely will: You shall do it. He shall do it.
(in laws, directives, etc.) must; is or are obliged to: The meetings of the council shall be public.
(used interrogatively in questions, often in invitations): Shall we go?
Usage note: The traditional rule of usage guides dates from the 17th century and says that to denote future time shall is used in the first person (I shall leave. We shall go) and will in all other persons (You will be there, won't you? He will drive us to the airport. They will not be at the meeting). The rule continues that to express determination, will is used in the first person (We will win the battle) and shall in the other two persons (You shall not bully us. They shall not pass). Whether this rule was ever widely observed is doubtful. Today, will is used overwhelmingly in all three persons and in all types of speech and writing both for the simple future and to express determination. Shall has some use in all persons, chiefly in formal writing or speaking, to express determination: I shall return. We shall overcome. Shall also occurs in the language of laws and directives: All visitors shall observe posted regulations. Most educated native users of American English do not follow the textbook rule in making a choice between shall and will. See also should.
and here is the definition of "should"...
pt. of shall.
(used to express condition): Were he to arrive, I should be pleased.
must; ought (used to indicate duty, propriety, or expediency): You should not do that.
would (used to make a statement less direct or blunt): I should think you would apologize.
Usage note: Rules similar to those for choosing between shall and will have long been advanced for "should" and "would," but again the rules have had little effect on usage. In most constructions, "would" is the auxiliary chosen regardless of the person of the subject: If our allies would support the move, we would abandon any claim to sovereignty. You would be surprised at the complexity of the directions. Because the main function of "should" in modern American English is to express duty, necessity, etc. (You should get your flu shot before winter comes), its use for other purposes, as to form a subjunctive, can produce ambiguity, at least initially: I should get my flu shot if I were you. Furthermore, "should" seems an affectation to many Americans when used in certain constructions quite common in British English: Had I been informed, I should (American would) have called immediately. I should (American would) really prefer a different arrangement. As with shall and will, most educated native speakers of American English do not follow the textbook rule in making a choice between "should" and "would." See also shall.
In the end, I have decided that you have failed to do proper research and have twisted things to say what you want them to mean. If you are a believer in Christ, I suggest you repent and ask for forgiveness because deception is a sin. Also, you just proved a point that I was trying to make that many have stated, "traditionalist who think all translations other than KJV are false, try to do whatever they can to prove other versions wrong." I am very disappointed and I am sure God is too.
Here is a classic case of someone with an agenda who refuses to see simple facts. Your own quotes, especially in the usage notes state that "should" and "shall" are used in different ways. "Shall" is used "to express determination," while "should" "can produce ambiguity." There is an element of uncertainty in "should" that does not exist in "shall."
But this is only the difference between two English words, the real question is which word more closely reflects the original Greek. The word in Greek is apoletai, which is a verb, third-person singular, subjunctive mood, aorist tense, middle voice and is literally translated "may perish." A subjunctive mood expresses a wish, a desire, or a possibility. Thus "may" or "should" expresses that it is a possibility. But "shall" by common English usage implies certainty which isn't true to the statement in the original language.
If you bothered to read the other articles on Bible translations, you would have found "Why don't you use the King James Version?" and "Which version of the Bible is most accurate?" in which I state that the King James Version isn't the best to use today. The point of the article is that the New International Version is not a highly accurate translation. I chose to compare it to other translations to avoid detailed technical arguments from the Greek, but if you are interested in these, I'm quite willing to prove my points. It remains significant that the New International Version in a number of verses expresses a different meaning from other versions whose goal is to give a literal translation of the text. This is something anyone can see by comparing translations, even when they don't know the details of the Greek and Hebrew languages.
I'm sorry for everything I said earlier. It's been a really long day.
Your apology is happily accepted.