My frustration is partly due to the fact that Hebrew is not my native language. Thankfully, Heschel took the time to explain in his book, "Between Man and God", that when Torah says, "Shema Yisrael, Adonai Eloheinu, Adonai Echad," the term "echad", in addition to referring to a compound one-ness (e.g. man and wife becoming "basar echad" or "one flesh), the term "echad" refers to the idea of solitariness or "only-ness".
In other words, when Torah says G-d is "one", it means that His reality is totally unique--He is all that there is and there is none other besides Him.
Without further ado, here's Heschel on this profound idea:
"Furthermore, doubts have been raised whether the term 'one' is at all meaningful when applied to God. For how can we designate Him by a number? A number is one of a series of symbols used in arranging quantities, in order to set them in a relation to one another. Since God is not in time or space, not a part of a series, 'the term 'one'' is just as inapplicable to God as the term 'many'; for both unity and plurality are categories of quantity, and are, therefore, as inapplicable to God as crooked and straight in reference to sweetness, or salted and insipid in reference to a voice' (Maimonides, The Guide of the Perplexed, I, 57).
God is one means He alone is truly real. One means exclusively, no one else, no one besides, alone, only. In 1 Kings 4:19, as well as in other Biblical passages, ehad means 'only'," Heschel, Between God and Man.