Want proof that Shir Hashirim really is a metaphor for the God/Jewish people relationship, not "just" a love song? Here's what convinced me. (credit to R' Yoni Grossman)
השבעתי אתכם בנות ירושלם, בצבאות, או באילות השדה, אם-תעירו ואם-תעוררו את האהבה עד שתחפץ
Crudely translated: "I make you swear, daughters of Jerusalem, by gazelles, or by the deer of the field, lest you awaken or arouse the love until is desired."
Now, people usually swear by God, their life, their soul, their honor, Satan - there is a short list of entities whom it is worth swearing to. Needless to say, gazelles and the deer of the field are not on that list. The phrasing is thus utterly incomprehensible...
Until you notice the pun. Gazelles - "tzevaot" - sounds a lot like "Hashem Tzevaot". And deer of the field - "ayalot hasadeh" - sounds a lot like "El Shadai". The verse is none other than a disguised oath in God's name, which would make perfect sense, and not in the name of a wild animal. If you didn't get it the first time, the pun is repeated with a different name of God. The choice of gazelles and deer to make the pun is in line with Shir Hashirim's general tendency to use metaphors from nature.
If two references to God in Shir Hashirim are in fact disguised through natural metaphors (and there is no other way to understand the verse), then perhaps there are others. Perhaps the entire book is such a disguised reference?