I don't see either Run of the Arrow or The Last Wagon as belonging in the first group. Fuller's film has a characteristic harshness in places but it's got that lost soul theme but I don't see it as noir as much as a study of identity and loyalty.
The Last Wagon is pure Daves, a wonderful, life-affirming movie that drives home an ultimately positive message but not noir, and for the same reason I'd drop The Hanging Tree out of the second tier. The whole drive is towards that's beautifully realized moment of renewal and spiritual rebirth at the climax.
I'm not sold on The Big Country being positioned so high either. There is a darkness to the relationship between Ives and Connors and the feud might be considered as supporting evidence, but again I don't get the sense of desperation that would increase the noir credentials.
On the other hand, Ramrod and Colorado Territory need to be bumped to the top tier, and I'd be inclined to shift Pursued in there as well. I think these are solid inclusions. Last Train from Gun Hill, for Douglas' intensity if nothing else needs to move up as well and I reckon The Naked Spur could be elevated. Finally, I'd place man With the Gun in to the second tier at the very least - the killing of De Corsia and the burning of the saloon alone would seem to demand that.