I was leaning almost towards lawful neutral for many of the same reasons, but I was having a hard time with it due to his obvious criminality and lack of an obvious code (except filling his pockets). I guess that take was influenced by Yojimbo as well, I see some of Sanjuro's Bushido in the Man With No Name, but it is a stretch. My view was definitely colored by many (including my own) steriotypical CN portrayals, he just seems too in control to be truly chaotic.
[spoiler]My primary reasoning comes from A Fistful of Dollars, as he sees both of the criminal families done in, leaving San Miguel with a relative peace, with the governments of Mexico and the United States coming in (I always presumed to fill the power vacuum). But then again, in For a Few Dollars More the Man With No Name is a bounty hunter, ruthless, remorseless, who seems less interested in bringing people to justice than in making money off of their capture (or more often killing). That said, everything he does is done to further his agenda, even when helping rob the Bank of El Paso. In the duel at the end it is difficult to ascertain his motives, because he gives Mortimer the chance to get revenge (the big reveal comes after, but clearly Manco knew something was up, given the pocketwatch) but in doing so he still gets his bounty. Maybe that one is one of those confluences of interest where the (well, presumably) good act and the self serving act are the same...but maybe not.[/spoiler]
I agree with your assessment of The Good, The Bad, and The Ugly, but with the addendum that I'm still not sure the chaotic descriptor fits. Regardless, he's a fascinating character.