Moving VHDX file attached to Failover Cluster "iSCSI Target" role with no downtime?

Good day,

The setup:
I have a Failover Cluster, each member of which is attached to a shared storage of two LUNs - LUN1 and LUN2.

LUN1 hosts a large VHDX file (of several terabytes) assigned to the "iSCSI Target" cluster role. This role, in turn, allows the same (or other) hosts to connect to this VHDX virtual drive by iSCSI and do some intensive reading & writing on it.

The problem:
I need to move the VHDX file from LUN1 to LUN2, while allowing its iSCSI clients working on it. I want to copy all its contents to the new storag, while avoiding situation, when I have to disconnect these clients during the copying operation to avoid changes made by clients being lost after the switchover of the "iSCSI Target" to the new copy.

Possible direction?
Now, Microsoft has a solution called "Virtual Machine Storage Migration" doing exactly what I need:

• Throughout most of the move operation, disk reads and writes go to the source virtual hard disk.
• While reads and writes occur on the source virtual hard disk, the disk contents are copied to the new destination virtual hard disk.
• After the initial disk copy is complete, disk writes are mirrored to both the source and destination virtual hard disks while outstanding disk changes are replicated.
• After the source and destination virtual hard disks are completely synchronized, the virtual machine switches over to using the destination virtual hard disk.
• The source virtual hard disk is deleted.

But unfortunately, as the name says, it's for virtual disks attached to VMs.

Is there any possibility to use the same technology for VHDs used by "iSCSI Target"?

If not, then it would be real nice to have such a feature.