Dee never called the angelic language Enochian. His own term was Angelical; the diaries also give Celestial Speech, the Holy Language, the Language of Angels, and Adamical, the tongue in which Adam named the animals, lost at Babel and now being restored. The association with Enoch is genuinely his: he titled one of the received manuscripts the Book of Enoch. The adjective attached later, and by whom is not established. Any account that has Dee practising "Enochian magic" is using a label from after his time.
The rest of him resists the categories too. He was the most learned mathematician in England, wrote the preface to the first English Euclid in 1570 arguing for mathematics as the foundation of the practical arts, trained the navigators of the northern voyages, advised the crown on calendar reform, and coined the phrase British Empire. His library at Mortlake ran to some four thousand volumes when the university libraries held a few hundred, and scholars came to it from across Europe. He also cast horoscopes for Elizabeth and set the date of her coronation.
None of this was in tension for him, which is the point Nicholas Clulee's study presses: the angel sessions were not a late collapse of a scientific mind but the continuation of one programme. Dee wanted the unified knowledge underlying the disciplines, his Monas Hieroglyphica of 1564 claims to compress it into a single composite symbol, and when books and mathematics stopped yielding it, he asked the angels, because the angels were the higher authority in the same hierarchy. Deborah Harkness's reconstruction places the conversations in the apocalyptic expectation of the period: he believed he was being given the language of creation because the end of nature was near.
He died at Mortlake in poverty, in December 1608 or March 1609, the parish register and the gravestone are both lost, and the date is not recoverable.