I would amend “ In the term’s original iteration, a neoconservative is someone who lived through the Vietnam War and believed the United States was right to fight it and should have won it.” to read “In the term’s original iteration, a neoconservative is someone who lived through the Vietnam War but did not fight in it or in any other war ….”
Of the neoconservatives you name (Kristol, Podhoretz, Glazer, Wolfowitz, Kirkpatrick), not a single one served in the military, let alone in combat. (Moynihan did join the Navy in 1944 but wasn’t engaged in battle — he did vote against authorization of the Gulf War, by the way).
Whether they’re described as liberal, conservative, or any other label, these neoconservatives are not hawks — they’re chicken hawks, and they have plenty of colleagues all along the political spectrum.