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.
“If you run, you are a runner. It doesn't matter how fast or how far. It doesn't matter if today is your first day or if you've been running for twenty years. There is no test to pass, no license to earn, no membership card to get. You just run.” John Bingham.