You can just clear the context or restart your Claude instance between tasks. e.g.:
> do task 1
...task fails...
> please update Claude.md so you don't make X mistake
> /clear
> do task 2
... task fails ...
> please update Claude.md so you don't make Y mistake
> /clear
etc.
If you want a clean state between tasks you can just commit your Claude.md and `git reset --hard`.
I just don't get why you'd need have to a separate Claude that is solely responsible for updating Claude.md. Maybe they didn't want to bother with git?