I think you're spot on in your synopsis. Much of Alchemy was a DIY process, with different Alchemists finding different solutions to the problems of the discipline. For the likes of Cagliostro and Melissino, the acacia as the prima materia and DMT as the lapis philosophorum prepared therefrom provided the solution. Although, another Alchemist might find a different solution altogether. For others still, no solution was found and a more meditative, internal approach was applied to the symbols. However, even those latter solutions point toward the idea of transcendence.
For example, the transmutation of lead into gold is, as you mention, one of the central themes running through Alchemy. For the Alchemists, every planet was possessed of a corresponding metal. The corresponding metal of Saturn, for example, is lead, and that of Sol, gold. Philosophically, this transmutation is generally understood as the transformation of the profane man of the senses into an initiated spiritual adept; that is, it is a process of illumination or enlightenment.
In the Kabbalah of Athanasius Kircher, a 17th century German Jesuit, this process may be represented as the progress of the initiate from the netivah of tau, the path of Saturn, to the sephirah of Tiphareth, the sphere of Sol; i.e., lead into gold. The heaviness of tau constitutes the first fledgling steps of the neophyte which will ultimately culminate in the attainment of Tiphareth’s brilliance as an adept. The so-called Christ center, Tiphareth is the symbol of illumination par excellence. While it is not the highest sephirah of the Otz ha-Chayyim or Tree of Life, it is certainly the most central and balanced of the ten.
In Jungian psychology, Tiphareth may be related to the transcendent function and to the archetype of the self, toward which the process of individuation strives. It is the coniunctio or union of opposites; the merging of the conscious and unconscious. After The Book of Abramelin the Mage, British occultist Aleister Crowley called this process the Knowledge and Conversation of the Holy Guardian Angel. Here, knowledge implies the carnal knowledge of sexual union, suggesting Tiphareth as the mysterious Bridal Chamber of the Gnostics spoken of in the Nag Hammadi Library.
The implication of the Alchemists’ operation of transmutation is thus nothing short of path to the self. It is the attainment of Tiphareth in Kabbalah and therefore of Christ in oneself.