As Hosea and Hagar are real people but also signify God and Israel, so it’s possible that Solomon and the Shulammite can be real people who also signify God and his people.
Once you grant this possibility, then you can ask of the Bible some questions such as:
1. Does the text of Song of Songs indicate a double signification as Hosea does?
2. Does the language of the text contain typological language that would lead you to think of book as pointing beyond itself?
3. Does the language itself oscillate between what makes sense for ANE lovers and what makes sense theologically between God and his people as Hosea might or as the prophets might like Ezekiel who describes God and Israel’s relationship as a marriage?
4. Does the mystery of marriage, which from its inception was always meant to double signify both human and divine marriage (Gen 2, Eph 5), require us to ask theological questions of the meaning of marital love?
5. Does the conclusion of Song of Songs in which love is likened to the flame of Yah (Song 8:6) suggest that the love in this story also tells us something about the love God?
These are the sorts of questions that I might ask of Song of Songs to help me adjudicate its meaning in accordance with the Apostles and by the help of the Holy Spirit.