The CRYSTALS-Dilithium digital signature scheme, selected by NIST as a post-quantum cryptography (PQC) standard under the name ML-DSA, employs a public key compression technique intended for performance optimization. Specifically, the module learning with error instance (A, t) is compressed by omitting the low-order bits t0 of the vector t. It was recently shown that knowledge of t0 enables more effective side-channel attacks on Dilithium implementations. Another recent work demonstrated a method for reconstructing t0 from multiple signatures. In this paper, we build upon this method by applying profiled deep learning-assisted side-channel analysis to partially recover the least significant bit of t0 from power traces. As a result, the number of signatures required for the reconstruction of t0 can be reduced by roughly half. We demonstrate how the new t0 reconstruction method enhances the efficiency of recovering the secret key component s1, thereby facilitating digital signature forgery, on an ARM Cortex-M4 implementation of Dilithium.