Make sure the two HA pairs have different sync-failover device group names.
On the primary add the other cluster of devices in the remote DC as peers.
Create a NEW sync-only group with those new members.
Synchronize only the NEW group.
You may find you now need to synchronize the local HA group to update the HA pair with the new information.
You will now see three sync groups. The local HA sync-failover group, the remote HA sync-failover group and your new global Sync-Only group. You will always see the remote HA group as unknown and that is expected as it is not part of this local HA group.
Once you have your global Sync-Only group synced across all devices then begin to add it to ASM as per that article.
In my experience ASM policy updates pushed out across the Automatic Sync Group have to be manually applied within ASM on the remote DC.