I am not as experienced a runner as you by any means, but I do run, and I run zero carb. I ran 10k yesterday, and although I ate a little more (I had a boiled egg extra) I was fine.
I run fasted, I drink only water during and after my runs, and after I have cooled down and showered I have a cup of tea with heavy cream. That is it.
I blog about running and zero carb if you are interested.