A method in a data storage system includes receiving a host I/O request from a host-side interface specifying a range of logical block addresses (LBAs) of a mapped logical storage unit (MLU) mapped through a device-side interface to underlying units of storage. Mapping information is obtained for extents of the underlying logical storage units mapped to sub-ranges of the range of LBAs. Sub-I/O requests for the extents are concurrently issued to the device-side interface based on the mapping information, subject to a throttling mechanism to manage performance. The device-side interface provides transfer initiation responses to initiate transfer of the extents, the responses being forwarded to the host-side interface to cause the host-side interface to transfer the extents in a transfer phase. The transfer initiation responses may be re-ordered as necessary to enable the host-side interface to transfer the extents in address order in satisfaction of the host I/O request.