> Dismantling the moon would disrupt the Earth's orbit

Not by itself. I basically agree with your broader point, of course, but on this particular detail, if someone's goal is to turn the moon into something like a Culture Orbital with the Earth at the centre*, the overall momentum of the system doesn't need to change.

* Or the old barycentre at the centre. This is also a terrible idea, please don't do this. Apart from anything else, mistakes are inevitable and large chunks of moon/O will rain down on us.