pazusoba is focused on beam search ever since the beginning. It might be the time to try something new. Monte Carlo, Simulated Annealing and there are more. I am fully aware of the issues with beam search.
The challenge is that the heuristic isn't great as it doesn't consider the future that much. Beam Search can find great solutions, but it takes time to do that. Some randomness is definitely needed, but it cannot be fully random. The heuristic is still good to determine if the current board is good or not.