Design a computational strategy for aligning homologous DNA sequences that have diverged significantly (over 30% mutation rate) since their last common ancestor. Discuss the limitations of standard dynamic programming methods like Needleman-Wunsch in this context and propose a profile-based or hidden Markov model (HMM) approach to improve alignment accuracy. Detail how you would calibrate the gap penalties and substitution matrices (e.g., PAM, BLOSUM) to account for the high divergence.