The Heh-Tzaddi switch is notoriously confusing and polarizing, but I'll try to approach it as simply as possible.
First of all let me say that I think nagasiva has basically gotten the answer correct, if i read his essay properly. But let me give my own take on it, and hopefully it will make sense.
First of all, ignore Eliphas Levi; he has little or nothing to do with it anyway. And ignore the Golden Dawn's revision of the planetary stuff - it also has little to do with it.
The 'occult' tarot has three sequences that are concurrent with each other; Tarot order, Hebrew alef-bet order, and 'magickal attribution' order, (which is connected to Hebrew via the Sefer Yetzirah).
If we take the Tarot de Marseille (TdM) order as a constant, we begin in the same place the Golden Dawn began. We then place the Hebrew letters on this order, and everything is great *except* that Teth lines up with Justice and Lamed lines up with Strength. This won't do, since Teth is also Leo the Lion, and Lamed is Libra the Balance, and these obviously should correspond to the cards having a Lion and the Balance on them.
So the GD switched those two cards in the TdM order. In effect, they were hijacking the Tarot order, and making it conform to the Hebrew alef-bet. This was illegitimate, because if you're grafting something onto the Tarot order, then you have to switch what you're grafting, not vice-versa. But this was their only mistake, and the adept could easily switch them back to layout the cards in TdM order instead.
One of the things Crowley did was to switch Justice and Strength *back* to their proper order, so that his Book of Thoth has the correct TdM order, where Justice is VIII and Strength/Lust is XI. Now the cards are in the right order, but two Hebrew letters (and their 'magickal attributions') are switched. No big deal.
But because of the phrase in the Book of the Law, Crowley felt he needed to switch the order of Tzaddi as well. It turns out the only sensible way to do this, with any equilibrium, is to switch the letter with Heh. And this is what he did, leaving the tarot in the TdM order, (Emperor as IV and Star as XVII).
The only problem is, he did not switch the 'magickal attributions' as well. This is where the confusion, and the mistake, occurs. In order to be consistent with the other switch of Hebrew letters Teth and Lamed, which KEPT their magickal attributions, the switch of Heh and Tzaddi must ALSO keep their magickal attributions. So it is fine to swap the letters for the Emperor and Star, but one must also swap the attributions of Aquarius and Aries as well.
By making the Emperor the letter Tzaddi AND the sign Aquarius, while making the Star the letter Heh AND the sign of Aries, the switch is consistent with what was done with the letters Teth and Lamed, and their attributes of Leo and Libra.
So the correct sequence as I see it is to maintain the TdM order, as the Book of Thoth tarot has it, while swapping the positions (on this sequence) of the letters Teth and Lamed, as well as the letters Tzaddi and Heh. At the same time, you must swap the magickal attributions of Leo and Libra, as well as Aquarius and Aries. Then, and only then, do you effect a 'double-loop' in the Zodiac, by switching the pair of letters/signs that are on either side of the letters/signs of Virgo and Pisces.
In short, one should keep the TdM order, but have Emperor/IV/Tzaddi/Aquarius -- Justice/VIII/Lamed/Libra -- Strength/XI/Teth/Leo -- Star/XVII/Heh/Aries.
The simplest way to make this change effective on the Crowley Thoth tarot deck is to swap the zodiac signs that appear on the Emperor and Star cards. The Emperor is Aquarius and the Star is Aries. Yes, it is true that the Emperor card has Ram symbolism, while the Star has Water-bearer symbolism. But you either make the proper switch so that all is symmetrical, or else you realize that due to the symbolism on the cards, (which is what caused the Justice/Strength swap), then one shouldn't have ever switched the cards in the first place!
But it is important to remember that the Emperor card never had overt Aries symbolism on it before, though the Star clearly had Water-bearer symbolism on it. One might think this would convince someone that the Aquarius/Tzaddi connection to the Star was correct in the first place, which is my own view on the matter.
So if I read nagasiva right, this is what he is saying, although I believe he is also advocating that the actual card of the Emperor should then in consequence be placed in position XVII and the Star should be placed in position IV. But I don't think this works at all. The Emperor needs to be paired with the Empress, and the Star/Moon/Sun sequence should remain intact. The Tarot de Marseille order is the correct one, and really shouldn't be messed with. If you want to graft Hebrew onto it, fine, but you make it all a mess when you change the order of the cards themselves, which are a specific sequence with specific reasons behind it, as occult as those reasons might be.
I would have to disagree with nagasiva that making the Emperor Aquarius and the Star Aries is somehow not fitting with their symbolism. Keep in mind that one of the symbols of Aquarius is the Man, and this would then be the Emperor, while the symbolism of the Ram/Aries is the beginning of the Zodiac, and the pouring of water from above to below on the Star card can represent the eternal regeneration of the cycle of the Zodiac. Besides the fact that the letter Heh, for Aries, is both the Mother and Daughter of the tetragrammaton, and these two feminine symbols can also be the two bowls of water, from above and below, mediated by the figure on the Star card.
The four tetramorphs, or symbols of the evangelists and the vision of Ezekiel, are said to symbolize the four Fixed signs and appear on the Universe card as well as the Hierophant card and the Chariot card. These are Man-Bull-Lion-Eagle, for Aquarius, Taurus, Leo, Scorpio. In Tarot terms, these would be Emperor / Hierophant / Strength / Death
This shows that both the Emperor and the Pope are subject to Death, but where does the Lion fit in? As Crowley rightly saw, Fortitude/Strength is better termed Lust; then Lust as Eros pairs with Death as Thanatos, and we have both the Emperor and the Pope, temporal and spiritual, subject to the Freudian pair of Eros/Thanatos. This kind of analysis is a bit more muddled if in fact the Star represents Aquarius, because the tetramorph of Aquarius is obviously the Man, and this fits well with the Emperor, while the Bull fits well with the pope. (maybe the term Papal Bull is not so coincidental?)
So one could use the tetramorphs as an aid to understanding the rightness of making the Emperor card related to Tzaddi and Aquarius.