But the quote from Romans 5:12 implies that it applies to man.... "death spread to all men." I have no problems with the idea that there is a point in evolution where there was a first man, who would've been Adam, whom God was prepared to give everlasting life to.
The Bible says man was created in God's likeness. Now, given that God is outside time and the universe, it doesn't seem likely that this is a physical likeness, but rather a spiritual one. God calls himself "I Am That I Am." Seems to me that the central likeness of man to God that separates us from the animals is the concept of "I am."
It is quite reasonable -- indeed, it is what I believe -- that Homo sapiens evolved to its present physical state, before Adam became the first human with the God-like realization, "I am."
The designation of Adam in Gensis 2 as being made in G-d's image refers to the fact that Adam, alone in creation, had free will-- and a mind to use that free will.
The souless men, by this theory, survived until the Flood-- interbreeding with Adam's line to create the Nefillim (Giants) .