A lower level cache receives, from a processor core, a plurality of copy-type requests and a plurality of paste-type requests that together indicate a memory move to be performed, as well as a barrier request that requests ordering of memory access requests prior to and after the barrier request. The barrier request precedes a copy-type request and a paste-type request of the memory move in program order. Prior to completion of processing of the barrier request, the lower level cache allocates first and second state machines to service the copy-type and paste-type requests. The first state machine speculatively reads a data granule identified by a source real address of the copy-type request into a non-architected buffer. After processing of the barrier request is complete, the second state machine writes the data granule from the non-architected buffer to a storage location identified by a destination real address of the paste-type request.