To be fair, there isn't a whole ton of fun game play to be had to explicitly achieve this goal. I tried a little cheese (and gained some PRs too) and a little "doing it normally" via the CZs, fighting against Sirius Corp. The latter was too slow to consider worth it, the former was very dull. Very, very, very dull. This was not game play.
In the end, I visited a Sirius owned settlement and took to murdering their staff. This took 3 round trips of a single extraction settlement and cost me 41k in murder bounties.
So, I'd have to say that it's not a particularly well-thought out game loop and agree somewhat with the OP irrespective of their method of completion. As an objective, much like the same basic ones in Horizons engineering, it's pretty thoughtless. I keep saying this but I consider the "complete x missions of y type" unlock process the finest Fdev have concocted to date. And not utilised enough. They're still a bit basic but at least they involve fun game play.