Hi,
it depends which License model you have active in your organizations. If you have per device licensing in both orgs, than you can do all by yourself and you don't need someone from support to transfer the license or hardware to the other organization.
Yes, you have to remove both MXs from the network in the old organization, than move it to the new org and add it to a new network... so you have to build a new cluster and configuration in the new network.
regards