I don't have my notes on the Hebrew letters, which I suspect are kind of flaky. I am happy with the astrological correspondences, though.
The classical order of the planets was based on how fast they moved across the sky. Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn. Starting from Malkuth (Earth) I assigned them in that order to the Sephitot in a left-right-middle pattern that made a pleasing arrangement.
I liked the effect that the middle "social" area of the tree (centered around tipheret) was bounded by mercury on the left and venus on the right. The Greek names are Hermes and Aphrodite, and a hermaphrodite is one that has both male and female characteristic. So male/female as a social organizing principle is present in the tree. I liked that. I talked about it being a cosmograph earlier.
The horizontal paths were assigned according to the elemental correspondences of the letters of the tetragrammaton: fire, water, air, (earth = malkuth, again).
Each astrological planet rules two signs (except the Sun and Moon, which rule only one). I got that from Agrippa. Moon: Cancer. Sun: Leo. Mercury: Gemini and Virgo. Venus: Taurus and Libra. Mars: Aries and Scorpio. Jupiter: Pisces and Sagittarius. Saturn: Aquarius and Capricorn. I arranged the signs of the zodiac on the diagonal paths so that they would connect with the ruling planet.
I found that there was a unique sequence of 28 steps that took you from Malkuth all the way through the tree and back, touching the sephirot in reverse order, the planets in ascending order, and the zodiacal signs in order (starting from Cancer). I don't think there is any faster route; this is what helped me fix the signs.
Well, not quite unique. You could interchange Capricorn and Aquarius if you wanted Aquarius to link Kether and Chokmah instead of Capricorn. It's a long story why I put Capricorn into path 11 - I'll post it later if you're interested.
The planetary assignments are highly traditional; I think 5 out of 7 of them agree with the Golden Dawn. I assign the Moon to Luna, though, instead of the High Priestess. The High Priestess gets associated with the Moon's sign, though - Cancer. And Saturn is the Hermit. I think I may have seen a version of the Hermit where he holds an hour glass instead of a lamp. Anyway, the Hermit is Chronos/Saturn - Father Time.
Some of the correspondences between the signs of the zodiac and the trumps were given previously in the thread. (Like Pisces = Hierophant). Some are just based on the image depicted; Libra = Justice, Strength = Libra. Virgo = Star. Aquarius (the water bearer) = Temperance. I thought a lot about interchanging Temperance and the Star; I kind of liked the idea of the virtues being close together, and there is water being poured in both pictures. But the Angel in Temperance isn't really a maiden (which is what "virgo" means), and I liked the abundance of wings in the cards for Temperance, the Devil, and Judgment at the top of the diagram.
Numerical balance played a role. Note cards 6&7, 4&5, 14&15, 12&13. Cards 2, 8, 11 and 17 also have a relationship (1 + 1 = 2, 1 + 7 = 8) that, oddly enough, works even if cards 8 and 11 are switched. With the position of the Emperor and the Hierophant you have the temporal and spiritual authorities of Late Medieval Europe in a dominating position in the social "middle" of the tree.
On the whole I am quite happy with my astrological correspondences. It is mostly the letters of the Hebrew alphabet that are giving me trouble, as I have discussed elsewhere in the thread. Oh, and the name of the arrangement. I can't think of a name that is suitably specific (e.g. not just "revised" or "reformed" or something) without sounding pretentious or egotistical (e.g. "gnostic" or "hermetic", or "Cheiromancer's"). "Cairo" comes from an arabic word for Victory, and sounds like the first part of my forum name, so I thought it would do.