Invaluable in this project will be the book Dictionary of Correspondences: The Key to Biblical Interpretation, published as a reference guide to all the symbolic relationships explained in Swedenborg's large corpus.
I expect this project to take up a medium-to-large amount of posts, and I'll probably make a post exploring the symbolic meanings of each book in the Book of Mormon (I'll probably squish Enos, Omni, Jarom, and the Words of Mormon together, along with similar things for other very short books). So, expect this project to be a major presence on my blog in the coming weeks and months.
A few caveats before I finish here: first, asserting the Book of Mormon's symbolic meaning doesn't rule out its literal meaning. According to Swedenborgian theology, every piece of scripture has at least three distinct meanings: its celestial meaning (corresponding to the Celestial Kingdom of heaven, a term familiar to any Latter-Day Saint), its spiritual meaning, and its literal meaning. The celestial and spiritual meanings exist in the literal meaning like a spirit in a body, and so it's important to remember that these deeper levels of meaning in scripture are vitally connected to the literal meaning. In fact, you might say that they need each other.
Also, please be wary of getting too attached to this interpretation. As I mentioned in my post Tips on Reading the Book of Mormon Effectively, any interpretation of the Book of Mormon will hinder your testimony if you grasp it too tightly, and this one is no exception. While it might potentially open new vistas of spiritual understanding, any way of understanding truth can get in the way of that truth if it becomes too "opaque," too complete in itself. So keep that in mind.
Also, if you're curious about Swedenborg's interpretation of the Bible, check out my post A Swedenborgian Testimony of the Book of Mormon, in which I compare it to the Book of Mormon's interpretation of its own symbols (in the context of Lehi's dream), and find them to be eerily similar.
So, fun times ahead! I'm excited to hear what you all think.