I've never heard of Typhon as a serpent either; he's described as having serpentine and reptilian features but not as a snake like in the Wheel card.
The Golden Dawn either didn't know or didn't care that Typhon was Greek. In their description of the Death tarot trump is the following: "This symbol represents the corrosive and destructive action of the infernal Fire as opposed to the Celestial—the Dragon of the Waters, the Typhon of the Egyptians, the Slayer of Osiris—which later yet rises again in Horus." Regardie,
The Golden Dawn, p. 211. In another place is the description of Ooma-Sathan, a.k.a. the Evil Persona: "
Omoo-Sathan. Typhon, Apophis, Set. The Evil Persona is a composite figure of the powers arising from the Qlippoth."
Ibid, p. 357.
Eliphas Levi also calls Typhon Egyptian. In Chapter 15 of his
Transcendental Magic, which deals with the Devil, is this: "Yes, we confront here the phantom of all terrors, the dragon of all theogonies, the Ariman of the Persians, the Typhon of the Egyptians, the Python of the Greeks, the old serpent of the Hebrews . . ." p. 288. (This could be one possible source where Waite made a connection between Typhon and the serpent.) And on p. 321 in his brief descriptions of the tarot trumps, for the Devil it says, "15.
Typhon, or the Devil."
W. W. Westcott, in Levi's
Magical Ritual of the Sanctum Regnum, p. 60, notes: "[Paul] Christian alleges that this demon represents the Typhon of Egypt, the genius of misfortune;"
It seems to me these different names were used mainly as symbols for the Devil and all having basically the same meaning. When Waite says he has presented Typhon in his serpent form, it seems possible to me he means Apophis. Even though this wouldn't technically be correct, since Typhon didn't have a serpent form, it seems possible that that's how he, and others from the same circles at the time, may have seen it; or he may have genuinely believed Typhon had a serpent form; or he may have just meant "I have presented 'the Devil' in his serpent form."
I've wondered too if the snake has some connection with the Lovers. Your explanation has given me something to ponder.