The step from seventy-two syllables to seventy-two angels has a name and a date attached to it.
Johann Reuchlin (1455 to 1522) was a German humanist, a Hebraist of the first rank, and the man principally responsible for making Jewish Kabbalistic material available to Christian scholars in Latin. In De Arte Cabalistica, published in 1517, he treats the seventy-two three-letter groups drawn from Exodus 14 as the names of angels, made pronounceable by the addition of suffixes such as -el and -yah, and lists them.
That is the hinge. The derivation itself is Jewish and medieval. The systematic reading of the results as a list of seventy-two named angels, each addressable, belongs to Christian Kabbalah, the sixteenth-century project of finding Christian doctrine confirmed in Jewish mystical technique, pursued by Pico della Mirandola, by Reuchlin, by Agrippa and by a long line after them.
Reuchlin is a serious figure and not an occultist in any modern sense. He wrote grammars, he fought a celebrated public battle against the confiscation and burning of Hebrew books, and his interest in Kabbalah was that of a philologist convinced the texts contained something worth recovering.
The consequence for this list is that its two halves have different owners. The counting procedure belongs to Rashi, the Bahir and the Zohar. The angelology built on it belongs to Renaissance Christian humanism, and everything downstream, the choirs, the sephirothic assignments, the zodiacal degrees, the psalm verses, the tarot, is built on Reuchlin's move rather than on the Jewish sources he was reading.
Sources that present the seventy-two angels as an ancient Jewish tradition are collapsing that distinction. The names are old. The angels are five hundred years old.