We present an optimized dual-stage CPR method based on pilot symbols and a blind phase search algorithm (BPS) for M-QAM coherent optical transmission systems, targeting an efficient hardware implementation. A comprehensive optimization of the key CPR parameters is performed, including, pilot-rate, number of test phases, angle interval and moving average filter size. The optimization process is validated through numerical assessment of the optical communication system performance using 16-QAM, 64-QAM, and 256-QAM modulation formats at 64 GBaud. The optimized dual-stage CPR is demonstrated to operate with a very low number of test phases in the second stage BPS algorithm. In addition, it supports more than 10× higher laser linewidth than the standard CPR based on pilot symbols. Besides, a reduction of more than 90%, in terms of hardware complexity is achieved with respect to the standalone application of the BPS algorithm. The optimized dual-stage CPR is also validated through hardware implementation based on VHDL, and its gate-level complexity is assessed for a commercial off-the-shelf Xilinx Virtex-7 FPGA.