One other thing to point out, as a response to part of the linked article: The sound “NG” gets its own glyph in many shorthand systems because it is its own consonant, not a combination of “N” and “G”. (In English, “NK” is typically just an “NG” followed by a “K”—not an “N” followed by a “K”—but it often gets its own symbol as well for the sake of brevity and ease of writing, just as we use a symbol for “CH” instead of having to write “T SH” every time.)
It’s likely that NG is missed out in some versions of the Major System because in English, it cannot start a word. (This is not true of all languages that have it.)
As for the 16th-c. shorthand texts mentioned in the article, they probably had nothing to do with the Major system, just as they little influenced the shorthand of the 19th century onwards; these were based on the English alphabet, not its sounds, although they frequently left off silent letters (like meddlesome GHs). See, for example, Shelton’s system here. Note that “i” and “j” are not distinguished, however, as they typically weren’t in the longhand of the time—the letter J being one of the youngest members of the Latin alphabet as used in English.
Someone may know better than me when research was first done into the phonetics of standard English. I would guess the Major system is pretty young in that field, and may have been on its bleeding edge at the time the system was first published. But there have been many publications on the subject in the past few hundred years.
(Edited because I messed up link formatting in one paragraph.)