I think I should elaborate on the military capabilities of the Patriarchate of Cape El. Hopefully TGR will come by at some point to go over his rebel sect, which I remind everyone is allied to the Patriarchate.
I've seen a lot of comparisons equating the Patriarchate to the so-called Islamic State; this is accurate in some ways and simplistic in others.
Like IS, Cape El enjoys the support of poor, religious young men who are willing to fight and die as martyrs for their faith. In addition, the Women's Brigades serve as nurses, medics, and in logistics. Unlike IS, the use of women in its military - though not in combat - increases its numbers. In some ways it is more organized than IS. Gunrei is interested in making this a functional state in more than name - to their best of their ability Cape El tries to keep power flowing as best they can, keep utilities functional, and so on.
Cape El makes money through high tithes, looting and the selling of stolen art, and taxes on non-believers. Pirates and fishing boats outfitted for combat patrol the straits; the Patriarchate controls territory on all three islands and intends to hold them.
Its land forces consist primarily of stolen military vehicles, technicals, and regular and irregular forces. It has likely acquired a few jets from military bases though not enough to establish air superiority. It has a high presence in social media and propaganda designed to attract Flemingovianists to its cause both in McMasterdonia and from abroad.
Regular forces entering Patriarchate-controlled land may find themselves in a quagmire. We know through McMasterdonia's previous use of chemical weapons that they have a stash of them - a stash the Patriarchate may very well have gotten hold of. In addition, irregular units such as guerillas and suicide bombers as well as improvised explosive devices make roads and cities difficult to police effectively.
The Patriarchate will not call it quits because it was defeated in open battle - it will continue to harass occupying forces with guerilla and suicide attacks until the easily-distracted and decadent secular populations at home grow tired of the war overseas. Videos of martyrdom are a propaganda tool for the Patriarchate, not a hindrance. It is not a rag-tag group of bandits harassing a government; Gunrei has brought the Royal Family nearly to its knees.