An apparatus includes a processing device comprising a processor coupled to a memory, with the processing device being configured, in conjunction with synchronous replication of at least one logical storage volume between first and second storage systems, to acquire an address lock for a set of pages of the logical storage volume starting from a particular page of the logical storage volume, to determine content-based signatures for respective pages of the set of pages, to compute an additional signature as a function of the content-based signatures, and to send the additional signature and a pointer to the particular page from the first storage system to the second storage system, so as to permit the second storage system to verify consistency of the set of pages in the second storage system relative to the set of pages in the first storage system. Such operations are repeated for other sets of pages.