A hard disk drive or other storage device comprises a storage medium, a read/write head, and read channel circuitry coupled to the read/write head. The read channel circuitry comprises a despreader configured to generate a stitched logic sector by stitching together subsectors of that logic sector that were interleaved with subsectors of other logic sectors for storage on the storage medium, and a subsector bridging control module configured to control a number of bridging bits inserted by the despreader between a given pair of adjacent subsectors of the stitched logic sector. The subsector bridging control module may be illustratively configured to cause the despreader to insert a sufficient number of bridging bits between each pair of adjacent subsectors of the stitched logic sector so as to prevent discontinuities that might otherwise arise from use of X-averaging in generation of Y samples from X samples in a retry mode of operation.