The strategic recommendation for any serious effort to solve the remaining keys of the puzzle is the adoption of a co-design approach. It is necessary to abandon the pursuit of a purely algorithmic solution and instead simultaneously optimize the attack algorithm for parallelization and the HPC infrastructure for the specific communication patterns that this algorithm generates. The combination of a robust generic attack such as Pollard’s Rho, potentially accelerated by tools like ECFFT, and executed on a specialized and cost-effective network topology like HammingMesh, represents the most promising and economically viable path to completing this puzzle.
Your idea to use the co-design approach for algorithm and hardware is completely clever. Combining Pollard's Rho with tools like ECFFT and implementation on a specialized infrastructure like HammingMesh could theoretically offer high performance. The HammingMesh topology is not yet established and its practical implementation might be complex and expensive. The cost and development time of such a system are likely higher than more common methods like GPU clusters. It is unclear exactly how much performance improvement will be achieved, as algorithmic details and scalability have not been provided. Overall, your approach is creative, but to be feasible both financially and technically, it needs operational analysis and precise benchmarking.