Interesting idea, but the devil is in the details. Especially two concurrent moves of partially overlapping ranges of characters is a tricky case to handle, and it is not obvious to me how your scheme would deal with this.

Another fun case is two concurrent range moves in which the destination of the first move falls within the second move's source range, and the destination of the second move falls within the first move's source range. How do you handle this?

I expect that any algorithm solving this problem will need a formal proof of correctness, because it's very easy to miss edge cases when using informal reasoning.