Nope, you're wrong about these lyrics still:
"Let me tell you the way it was, back when I was a different man, back when I didn't have a clue who I am"
Grammatically, it SHOULD be "was". The line is NOT about him changing or who he is as he's singing the line AT ALL - it's about who he WAS then. Going back to "Why God, Why?" he was confused about his role in the war, and who he was as a person that fit into that - THAT'S what he's singing about there. There is no question that the line is referring to the past, NOT about who he is as he's singing.
Additionally, he doesn't know who he would be in the future, obviously, so singing that he didn't know who he would become isn't just grammatically incorrect but redundant and meaningless. In addition to the tense issue, "man" and "am" don't rhyme (and I know it's followed by "damn" and "Vietnam" - but those couplets are separate from this one.)
I actually read this line to my 7th and 8th grade students today, and almost without exception they recoiled at the grammar and were EASILY able to point out the verb tense shift and why it didn't work...
Hi, Shirley Temple Pudding.