You list three left-leaning news organisations, and expect their biases to cancel out? Wouldn't they reinforce each other?
But this is not about right/left anymore - the scary fact (and becoming patently obvious to more and more people) is the fact that all "mainstream" media is pro-establishment (whether it is left or right is less important). That's why outlets like Breitbart, warts and all, have been gaining so much popularity.
Breitbart isn't the anti-NYT, it's the anti-Daily Kos.
Pretty much the only readable right wing media is foreign - but if he had suggested The Economist or the Financial Times you probably would have called them left-leaning too...
If you're after other right-wing UK publications you could try the Daily Telegraph or the Spectator.
I could not believe my eyes when I saw The Economist devoting a full page to Trump's badly-fitting suits and overly-long ties, but musing over Clinton's numerous corruption scandals, because she is the preferred globalist candidate.
I am sad that even The Economist has fallen - I have been a subscriber for 25 years. Perhaps not much longer.
Almost any combination will omit some political stance. I don't believe that political viewpoints are binary, or even that they vary only along a single dimension.
I can't go to CNN (what most on the "right" would consider "left") most days without seeing some headline about Trump unaccompanied by a headline about Hillary, in what I can presume is an attempt to be "balanced". The headlines are crafted to make things look equally revelatory. But when you read the articles you find that one is a serious strike (saying shocking things on a mic), and the other is usually a non-story, ie. leaked emails showing the candidate saying pretty much exactly what their public stance has been all along.
For instance an event where an old man drives his car into a wall. A neutral headline could be "Old man drives car into wall". But the problem with this is that a lot of people will now assume he drove it into the wall because he is old. So a better neutral headline would be "Man drives car into wall" and then the article has to explain the reason. This is a very subtle change but makes a lot of difference.
Now lets say an old woman drove her car into a wall: "Woman drives car into wall". A lot of people think women are worse drivers than men, so this will already be a sensational title for some.
A good read about this is "Why you should stay away from news" from Rolf Dobelli.
However, there is absolutely a difference between journalists attempting to report news in a neutral way and journalists intent on spinning news to forward some agenda, even to the point of using strategic omissions and what not to completely mislead the reader about a conclusion.
Moreover, a reasonably intelligent human can (and should) read a variety of new sources (that at least attempt to be unbiased) and generally can get an idea of what actually is going on. When you read 3 different versions of the same news story by BBC, NPR, and NYT (for example), then hopefully the biases sort of cancel out and you get something closer to the truth.