For instance the first article about ju-jutsu and judo that was written by Jigoro Kano and translated into English by T. Lindsay in 1888, has used the spelling "Jiujutsu", i.e. neither "jujutsu" (as written in this article) nor "jiujitsu".
In Japanese kana, in the 19th century, before the spelling reform that happened after WWII, the spelling was "jiyuu-jiyutu". The Japanese spelling might have suggested the writing of an "i" after "j" in the Latin transcription.
In the corresponding Latin alphabet spelling "jiu-jitsu", the reason why a "u" has been preserved from "jiyuu" but no "u" has been preserved from "jiyutu", is likely to have been because the first "u" is long, so it is pronounced clearly, while the second u is short, which in modern Japanese is pronounced without rounding the lips, so it does not sound like a "u". It also does not sound like a "i", because it is a back vowel, but English or French do not have this vowel, so they can render it only as either "u" or "i", and it appears that the choice has been random, because all variants are encountered in the old publications.
So there exist both "ju" and "jiyu" and they are distinct. In "juu-jutsu" there are only "ju", there is no "jiyu" (the latter can appear only in compound words).
Before WWII, in kana there was no distinction between "ju" and "jiyu" (there was no small "yu"), so you had to know that the word written as "jiyuujiyutu" must be pronounced "juujutsu", in the same way like you had to memorize many other differences between the old Japanese spelling and pronunciation (e.g. yahara => yawara, osahe => osae, kuwatu => katsu and so on).
Isn't that why English words ending in -t or -d get transcribed into Japanese with a final vowel of -o rather than the -u that is used for other final consonants?
The kana syllables are grouped by their consonant, so a direct transliteration would use the same Latin consonant for all kana in a group, e.g. "ta-ti-tu-te-to", but when it is desired to suggest the English pronunciation, like in the Hepburn transliteration, that corresponds to "ta-chi-tsu-te-to".
Before WWII, the kana spelling corresponded to a much older Japanese pronunciation, from about one thousand years ago, so there were much greater differences between spelling and pronunciation. So in my examples, what was written "yahara" was pronounced "yawara" and today it is written like it is pronounced, what was written "osahe" was pronounced "osae" and today it is written like it is pronounced, what was written "kuwatu" in kana had been earlier pronounced as "kwatsu", then the pronunciation has become "katsu" (= life) and today it is written "katu" in kana and "katsu" in Hepburn transliteration.
Even when you know some Japanese, reading any book published before WWII can be difficult, because many kanji used before have been replaced with others and the kana spellings of the old kanji can also be confusing because they are different from the modern spellings too.
You are right about the transliteration of English words into kana.
This seems unlikely. The pronunciation was tsu before WWII. But the organization of the syllabary strongly suggests that the pronunciation was once tu.
I don't know to what degree the syllable 'tu' is viewed as impossible in Japanese as opposed to merely nonexistent. (Compare Mandarin, where (as in Japanese) there is no syllable /si/, but it's not especially difficult for Mandarin speakers to pronounce /si/.) I'd be interested if you knew.
Or in other words, complete nonsense. You can't answer a pronunciation question by appealing to spelling conventions, particularly spelling conventions that are completely divorced from the reality of pronunciation.
Apropos of nothing much, where does that first I come from in "jiu-jitsu"? It's not present in the Japanese, but for some reason it appears in Portuguese even though the original vowel is a monophthong.