Pondering this idea further, there really is a difficulty in the fact that the level at which this sort of corporate politics functions in Kaalakiota is with its shareholders (familial and institutional) and that there is no current in-game means to engage with those characters added to the fact that even though there might be grave disagreement with the reforms of Heth within Kaalakiota, it would not mean that it would lead to outright
violentdisagreement. Such matters are again, the concern of the shareholders and the expectation would be to carry out the expected duties in the public arena, especially for those who consider themselves military professionals. The means of dissent would be kept in private to such an extent that externally, the corporation would remain indistinguishable from any other loyal subsidiary of KK.
There's also the undeniable fact that while there are legitimate concerns regarding Heth's policies, he has accomplished what any loyal Kaalakiota citizen would want: a Kaalakiota CEO leading the CEP and the State as its Executor and dictating its policies which (at least in their view) is the rightful place of Kaalakiota and its citizens.
As such, I think the best option is to push any political aspects of a potential Kaalakiota (perhaps with a nominal Wiyrkomi/Lai Dai/Patriot) aligned corporation and play the angle of being the consummate private military professionals who will prosecute their duty, tasks and most importantly their contractual obligations with the simple philosophy that what is good for Kaalakiota and the Patriots is good for the State and what is good for the State is the only moral and ethical imperative of any importance. There may be objections to that philosophy but frankly opinions count for nothing when the corporation is beholden only to its shareholders and its clients.
From that standpoint the objective will be to explore and build upon the, "Ronin" type mercenary culture in the State; the conduct of corporate diplomacy with high-explosives; and all that violent and dark cyberpunk-esque element of the State done with a Patriot twist. More a home perhaps for "Bad Caldari", the ones that live on the fringes of State society for one reason or another and hired by the company because men and women whose loyalties can be bought out are those whose lives can be easily expended in the name of Kaalakiota and the State and who would fit in far better in the darker world the corporation is envisioned to operate.
Far easier to leave what happens to Heth and Oiritsuu with CCP themselves in the long-term and maintain a degree of centrism and staunch loyalty to Kaalakiota than being concerned with what there is no real power or ability to change in-game.
The real issue I come up against though is that by its nature it would require a degree of duplicity (publicly presenting itself as toeing the current expected party lines whilst privately working against
The main problem with 'knife-fighting' ideas in Megacorps is that many things have changed greatly after Heth reforms, and you don't earn your positions by relatives, conspiracies and skullduggery anymore, but rather by your merits.
I will respond with this:
...They're fully aware, though, that this state of affairs won't last forever, and they're quietly assembling plans to ensure that when he is brought down, the Practicals won't find themselves hamstrung by the other corporations. If in the end they have to topple Heth themselves, then that's what they'll do. In the meantime, they're content to beat the war-drums and use the fighting as a cover for their other activities. (Link)
I could also point out just off the top of my head, the assassination of Heth's right hand man Janus or hell, maybe this:
Each great family maintains their own personal army to protect their private interests from other families, though unlike the relatively more well-known conflicts between the Big Eight, such confrontations occur behind-the-scenes of Caldari society. In many ways, these great families are significantly disconnected from the Caldari masses while still exhibiting massive influence over them. It is commonly the case that the great families will be the ones who influence a megacorporate board’s decision as to who they appoint next. Often when attempting to place their kin in position of CEO, internecine feuds and disputes will erupt between these great families, independent of the cross-corporate conflicts
To counter your assertion that Heth and the CPD have eliminated the back room politicking in the State that occurs behind the scenes. In the end, the power Heth and the CPD wields is
because he is the majority shareholder and CEO of Kaalakiota, not the other way around and he still has to go up against individuals, families and institutions that are powerful, wealthy and have their own interests because that's just how the State works.
I think even Heth understands that there's probably no better way to get himself killed than to threaten those families and institutions to such an extent that they collectively decide he's a greater problem than each other.
Edit: There's also the fact that if Heth and CPD were attempting to "reform" the power that wealthy families have over State Megacorporations it would mean, for one, at least being in direct opposition to the Seituoda Family of Wiyrkomi which last I checked has not occurred. Unless I might have missed something lately?