You could bring WTR into the alliance. Both entities are patriotic in alignment they just (to me) seem to have different views on how to do things so no matter who wins recruits corp wise the whole is strengthened and you can have some internal struggles/debates about how to do things etc to boot.
Pyre Falcon is a Kaalakiota Loyalist organization and it was intended as a vehicle to explore the particular culture, philosophy and operational ethos of Kaalakiota as a whole. There remains, even sans Heth, noticeable if subtle differences between how Kaalakiota generally operates from Wiyrkomi -- in short, you don't get to be top dog in the State as KK without a willingness to play corporate realpolitik better than all your rivals.
The reason why Oiritsuu and Heth, I think, would have been backed to some degree by their peers in Kaalakiota is because they promised what the majority of KK citizens want -- strength and power -- in their own ways. It's not particularly for its own sake, but rather because of history and tradition behind the company: Kaalakiota is the biggest, the best, the most powerful, the holders of the legacy of Sobaseki, the true bearers of the Caldari vision, the guardians of the State. It's a combination of nationalism, patriotism, corporate pride, ruthlessness, pragmatism and cynicism that drives Kaalakiota in my mind perhaps with Heth indicative more of the former and Oiritsuu more of the latter.
What this means for Pyre Falcon is that if a plan can be framed in a patriotic context of, "Serving the interests of Kaalakiota Corporation and the Caldari State," then the question of, "How do we proceed with the plan?" Will be responded with: By whatever means necessary.
How I've viewed Wiyrkomi doing business tends to be far less ambitious perhaps, centered on more conservative and cautious business practices and the latent but strong cultural elements of being what continues to be traditional Caldari family owned enterprise - and everything that goes with that.
Besides the point of course that I think from an RP perspective, it's far more interesting to see the creation of identities along, "Kaalakiota Patriot," "Wiyrkomi Patriot," and, "Lai Dai Patriot" which leads to more attention being paid to the different culture, history and outlook of each Mega itself than just a homogenization as, "Patriots".
In this, I think the WTR is a good thing, because it has the potential to explore what it means to be loyal to Wiyrkomi first and foremost. Besides it's not like we're not going to be in the same neighbourhood if you want to fly together and shoot Feds, or just RP with the people in Pyre Falcon.