I haven't seen The Swimmer, though I wish I had just so I could have voted against NOTLD.
I haven't seen Hearts & Minds, but not only is MASH a great movie, it's the epitome of what you're after in this tournament, so you shouldn't be too disappointed.
I agree with George here. Hearts and Minds, regardless of its merits as a film, is a documentary that really is not particularly innovative and did nothing much to change the state of American filmmaking.
M*A*S*H, regardless of its merits, was one of a handful of Altman films that really did help establish the independent filmmaking of the 70s and, while not groundbreaking, certainly told a story in a way that was very different than established Hollywood methods. That it was a hit, gave Altman enough power and credibility to make films like McCabe & Mrs. Miller and Nashville, both very fresh and innovative (and both I think better than M*A*S*H.