Efficient node repair is a central requirement in distributed storage systems, particularly in high-rate erasure-coded deployments where repair traffic directly affects network overhead and recovery cost. Piggybacking codes reduce the repair bandwidth of MDS array codes while keeping the sub-packetization level small. However, existing piggybacking constructions often rely on restrictive piggyback-function designs to preserve the MDS property over small fields, which limits their repair-bandwidth reduction. We propose {\em conjugate-piggybacking} codes, a new class of MDS array codes that jointly design piggyback functions and conjugate transformations under small sub-packetization. The proposed construction improves repair efficiency while preserving the MDS property over moderate field sizes. In particular, it enables some parity nodes to achieve optimal repair bandwidth and reduces the overall repair bandwidth compared with existing piggybacking-based designs. We analyze the MDS property and repair bandwidth of the proposed codes and evaluate them against existing piggybacking codes under high-code-rate settings over $\mathbb{F}_{2^8}$. We further conduct a repair-traffic simulation under uniform single-node failures to quantify the expected traffic reduction in storage-oriented settings. The results show that our construction consistently achieves lower repair bandwidth than related piggybacking codes and reduces expected repair traffic compared with conventional RS repair. These gains are obtained at the cost of a slightly larger field size, revealing a practical trade-off between repair efficiency and field-size overhead for high-rate distributed storage.