A storage system includes a controller and block-based storage device(s) that include LSA blocks arranged as a log structured array (LSA). The controller creates a first and second LUN, each including LBA locations. The controller assigns the first LUN to a first host and the second LUN to a second host, accumulates first host data associated with a first LBA location of the first LUN, writes a block-size worth of such data to a first LSA block, and maps the first LBA location to the first LSA block. In response to receiving an ODX Copy Offload instruction, the controller determines the first host data should be migrated to a target LBA location in the second LUN, determines the first and second LUN are exclusively mappable to the same LSA, maps the target LBA location to the first LSA block, and unmaps the first LBA location from the first LSA block.