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[GoodLeave]

That's all well and good if the batsmen were attempting a run or were making an effort to back in, however i'm pretty sure there's parts of the laws you've not quoted that state you cant be run out if you are in affect starting to leave the field in the mistaken belief that you are out. So if every letter of the law is followed, he's still not out.

Very true. I just looked up the laws around no balls and chose the two sections that seemed relevant.

I guess it depends on where the pavilion is, OP says he was halfway down the track? Was he genuinely going for a run or was he heading towards the pavillion? End of the day, it's a game 

[meats]

That's all well and good if the batsmen were attempting a run or were making an effort to back in, however i'm pretty sure there's parts of the laws you've not quoted that state you cant be run out if you are in affect starting to leave the field in the mistaken belief that you are out. So if every letter of the law is followed, he's still not out.

The OP said they had crossed so the new bat wasn't on strike so I would say they were actively looking at taking a run in this instance.

[tim2000s]

It's all a bit tricky as we weren't there. I think the critical points are:

1. The umpire is supposed to "call and signal no ball".
2. You can be run out off a no ball.
3. Had the batsmen crossed as they were going for a run, and mistakenly thought that the striker was caught out?
4. If the striker thought he was caught, was he meandering after crossing because he incorrectly assumed he was out?

If the situation is point 4, and the umpire hadn't called "No ball", then it should be declared "dead ball" and the innings should resume with no run given and the batsmen returning to their ends.

That would really be in the best spirit of the game.