We can either try to brute-force the pkeys, and/or we can try to reverse-engineer (also by some amount of brute-force, I guess) and recreate the process by which the pkeys were created...
I just can't quite grok what's happening here

Any help would be much appreciated

Let me explain more...I use a trial-and-error method a problem-solving approach where you systematically try different options or solutions until you find one that works or achieves the desired result.
It involves a process of experimentation and learning from your attempts, and it's often used when you don't have a straightforward or known solution to a problem.
You start by making an attempt or trying a particular option, strategy, or input.
In this case it is a random seed.
After your attempt, you carefully observe the results and outcomes. You gather information about what worked and what didn't. You analyze the results to determine if your attempt was successful or not. If it was unsuccessful, you analyze why it didn't work.
Based on your analysis, you make adjustments to your approach, such as trying a different option, changing a parameter, or using a new strategy.
You repeat the process, trying the adjusted approach or a new option. You continue this cycle until you achieve the desired result or solve the problem.