Sorry to bump this behemoth back into life, .... but I've been digging into this whole mess lately, and would like to take a stab at summarizing this in as clear a manner as possible (and to verify I have this correct in the first place!)
1: Prior to the Golden Dawn, the generally accepted trump order was that of Eliphas Levi (I won't bother detailing the earlier arrangements), which has the curious quirk of placing '0 - the Fool' between
XX and XXI,
To make it quite clear to initiates that they did not understand the meaning of the card called The Fool, they put him down between Atu cards XX and XXI, for what reason it baffles the human imagination to conceive. They then attributed the card number I, the Juggler, to the letter Aleph. In this simple yet ingenious manner they got the attribution of every card, except The Universe, XXI, wrong.
2: Golden Dawn makes two key changes; '0 - the Fool' is promoted to the first of the trumps, advancing all other cards by one letter (which also brings the letter=zodiac attributions in line with the Sepher Yetzirah), and 2: Mathers swaps the ATU images around for Strength (Fortitude) and Justice to 'fix' their images with the zodiac, which pretty clearly depict Leo/Libra. The Roman numbering is preserved by natural order of the cards.
3: "Tzaddi is not the Star", and here we are. Crowley swaps the Emperor & the Star cards, keeping the roman numbers IV & XVII attached to them, and additionally 'restores' the original numerals of Justice as VIII and Strength as XI (his reasoning undoubtedly reinforced by his Qabalistic interpretations of these numbers). It is this arrangement of the 'original' roman numerals, when the zodiac cards are ordered by their hebrew letters, which gives rise to the infamous 'double loop' pattern.
It should be noted though how this change was made, for Crowley has not moved the hebrew letters around for the Tzaddi switch - as HEH remains on path 15 and TZADDI on path 28 - but he has swapped all the other attributes of the Tarot cards: the ATU, roman numeral, and associated zodiac sign. In switching the zodiac signs with his change to IV & XVII, however, he has broken with the Sepher Yetzirah attribution of TZADDI=Aquarius and HE=Aries, and created a one-sided 'loop' in the zodiac.
Situation sound about right?
This is most clearly illustrated as a whole; (see attached image);
center -> out: path#, hebrew letter, zodiac, atu, roman numeral