Changed Block tracking used as ChangeID for identification, which consists of a UUID and a sequence number. If a backup application first backs up a virtual disk, it has no knowledge of the UUID and will default to a full backup (sending an asterisk to the API instead of the ChangeID). Assuming that the backup application stores the ChangeIDs for the different virtual disks with the virtual machine to which the virtual disk is connected, I'd expect that attaching the virtual disk to another VM will result in a full backup. What may work - if this is not desired - is to keep the current VM and only replace its OS virtual disk with the newly create one. This way the backup should only need to run a full backup on the OS virtual disk.
André