The "tree" used depends entirely upon what is to be done with it. If one uses the Golden Dawn version of the tree of life, its not a matter of which one is the right one, its a matter of what is to be done with the tree given. Is is to be used for inner alchemical work? is it a Kabbalistic one? Are you using the tree in conjunction with Astrology like the OGD recommends? These questions are essential to figure out "why" one is using a particular tree. It is simply a map and there is no wrong way to get to where someone is going. That being said Kircher was a avid catholic, he detested anything NON Catholic, so its entirely possible in the perpetuation of his version of the Tree the correspondences were destroyed because of the reasoning behind Kircher. Although this is just speculation at best.
I would simply say to anyone using the Order of The Golden Dawn system, to evaluate what the symbol really means. To look at it as not a algebraic symbol of spirituality and intellectual curiosity , but as a real working guide to show different perspectives in everyday life. That was the original purpose of the Sefer Yetzeriah to bring to light the Metaphysical content behind words to the front of a practitioners conciousness. This kind of attention makes the letter have more than just a "symbolic" meaning but the letter will take on a "mind" of its own, a sort of intellegence that seeps through everyday life. Although the real benefit of the Metaphysical content in specific relation to letters comes by extensive knowledge of the Hebrew words and is similar to Vajrayana Buddhism when the Tantric practitioner realizes that all the words in a Mantra are symbolic of seed ideas and powers behind the word. This they call the "Speech Mandala" and it makes the words impregnated with meaning. When taken in a ritualistic context the words of the ritual take on the powers of the Metaphysical system of the letters.
GTC