This a pretty cool idea although the problem of defining 'right' and 'left' sources obviously rears it's head (who will watch the watchers).
It made me re-remember an idea I had a while back. It would be an interesting exercise to take a New York Times news story and re-write to remove POV to the best of your ability. Perhaps add important details that they left out. Fer sure change the wording to remove loaded words and phrases. Get a couple of dozen friends to help out and you could do your own private newspaper.
It doesn't deal with the problem of purposefully unreported stories or your own bias creeping in, but would be a fun thing to try.