This is a pretty incredible piece of work.So, I know the OP mentioned a few times he didn't want to go into the exact specifics of the POD, but as far as Northern Ireland is concerned, let's give it a try. While the running joke here is how much of the early chapters of the TL parallel the Spanish transition to democracy, only to speedrun right into austerity politics, Northern Ireland is the one thing that stands apart.
From what we know from the TL and the author's comments, the following bits are (rather loosely) canon:
*The general thrust of it, as just mentioned, is that of the Troubles but with a lot more dead people, culminating in a peace process of sorts akin to OTL that parallel the Cardiff Accords; as much as we can dispute it, that's the limiting framework; in addition, the UK-Ireland relationship is poor because of NI being under military occupation (pre-existing tensions in Northern Ireland here could suggest a parallel with Taiwan under the GMD or - minus the colonialism bit - the various attempts by the Kremlin during the Cold War period to limit the spread of alternatives to the existing Marxist-Leninist ideology, complete with human rights violations), further reinforced through having an NI veteran as Defence Minister in the Johnson Government, Hague's predecessor in National being a former Governor of NI, and Ireland proper as one of many havens for exiles (hence why, ITTL, Harvie hiding out in Dublin makes sense - not to mention symbolic value as the seat of the British government-in-exile during the Junta years)
*We also know, from the OP, that repression in Northern Ireland was very harsh (along with Scotland and Wales), leading to a renewal of the IRA from '68 onwards (so NICRA would be a cause for alarm on both sides of the Irish Sea, from the POV of the Junta and from Stormont), which suggests a parallel between Northern Ireland and the Spanish peripheral nations (considering the history of bombings and all that, including the formation of the World High Jump Record Holder meme, the closest parallel here would be of the IRA = ETA and hence NI = Basque Country), but considering Irish history and particularly NI's history in all its complexity, such a simplistic narrative will not do - not when Loyalist paramilitaries are still a thing alongside Civil Assistance, as well as both the Troubles and the Basque Country forming models for the conflict in Scotland that led to where Scotland is now ITTL
>Furthering it more is NI's central role during the British version of 23-F, as one of the main area of operations alongside London - not to mention reigniting sectarian tensions yet again
*We also know - much like in 1964 in Brazil (with the formation of ARENA [pronounced ah-RAY-nah] and the MDB) and Francoist Spain (with the formation of the FET y la JONS) - that the National/SDP formation was not entirely consensual (indeed, National was formed out of a motley crew of parties, including the UUP), which not only colors NI politics ITTL (alongside the existence of SF and the SDLP - as with OTL) but also seeks to conform NI to the British political norm, governed like the rest of the UK (even with its own quirks)
Considering all that, that suggests some parameters.
*The first concern for the Junta, in order to stabilize its situation post-coup, is to ensure the rest of the country falls in line. Northern Ireland by design is distinct from the rest of the UK insofar as (because of the 1920 Fourth Home Rule Bill) it has its own parliament. Under normal peaceful circumstances (pre OTL/pre-POD) that would mean Westminster and Whitehall could allow it to fall off their radar as it could take care of itself (no matter how horrendous it was); in the context of a military occupation, with Northern Ireland holding the same status as the rest of the UK and holding a land border through which dissidents could escape, the Junta would see it as a security risk.
*Then there's the matter of O'Neill's Government and the rise of NICRA, both of which are anathema to the politics of fear that governed NI up until the POD. While both were ultimately necessary to ease some of the tensions going on (even if they were years ahead of the time, although NICRA was in parallel with other similar events going on worldwide during the '60s), it also creates a problem for the Junta, both as a potential bastion for opposition and also (as you noted) if things went wrong to make Republicanism (with a capital R) a cross-community thing. From a Unionist POV, that cannot be allowed to happen, as that means the old sectarian fears would be rising up again.
*Finally, there's also the left-wing turn the Officials took towards a more Marxist line. From the point of view of dissidents, that is unacceptable as it's basically abandoning The Struggle (TM/MC) - not to mention that by that point, Ireland proper was going its own way, with things going on in Belfast et. al. a minor part of one's peripheral world-view. (Not when there's more exciting stuff going on, like the introduction of television, free secondary education, and the beginning of Sean Lemass's economic reforms, for instance.)
So the Junta would need to find a way to tar anything "Irish" with a broad brush, whether or not it was accurate, and try to condition the people to accept British military rule while still having an armed struggle going on that is still recognizably similar to OTL as a sectarian conflict gone pear-shaped. Anything that would be seen as uniting Northern Ireland together against the Junta, altering its political and social divisions, would need to be prevented, full stop. One part of this would be exploiting sectarian tensions and tarring with a broad brush its left-wing opponents (NILP, the IRA/SF, etc.) as "Communists" and terrorists. But it needs to be much more than that to bring NI on board with the rest of the UK (and hence making the NI conflict reasonably similar to, if not exactly like, the Troubles, probably with bringing forward both the OTL events of 1969 and 1972, probably even having them blend into each other).
On one hand, the Junta would basically be functioning like apartheid-era South Africa when it comes to exploiting sectarian tensions (including adopting a very broad definition of Communism as being anti-Junta and consolidating and increasing the repression of Catholics through a similar battery of laws as apartheid South Africa unleashed in the 1950s and/or even a strengthened variation of the old Penal Laws). As a possible focus for anti-Junta resistance, that would mean increased repression on coupled with co-opting of the Catholic Church (in which case the Junta would be in good company with certain Latin American dictatorships). Armagh would be a bloodbath all throughout the Junta (including the Church of Ireland as well, as it became more anti-Junta), as the mother seat of Christianity in Ireland.
On the other hand, the Junta would need to eliminate all other alternative definitions of Unionism (funnelling such dissent leading towards the transition out of Northern Ireland and into the rest of the UK or with the British government-in-exile and prevent possible cross-community "contamination", creating a cordon sanitaire around Irish nationalism and retaining the pre-O'Neill status quo. (In effect, what would ultimately IOTL become Alliance should not be allowed to form. but instead funnelled into a moderate nationalism led by the SDLP - making it a NI counterpart to the SDP on the Mainland - once liberalization under Hill-Norton starts.) So the Junta would need to engineer a split within the UUP in order to create a NI wing of National by scapegoating O'Neill et. al. as traitors to the Protestant faith and the British Crown (that Protestantism in Northern Ireland is pretty diverse would be immaterial to a Junta seeking "stability", but the vitriol is such to prevent the Catholic Church from becoming a cross-community arena of anti-Junta resistance), not to mention ravaging the NILP so that it too becomes part of National purely on the grounds of maintaining Unionism and Protestant supremacy. NI's Home Rule Parliament and Government would also need to be forcibly abolished (and hence the 1920 Government of Ireland Act repealed and replaced with something else), necessitating a period of direct rule (reverting to the 1801-1920 status quo) before a provincial government (under military occupation) would be set up.
Would it be difficult to pull off? Probably, but that's how having the *Troubles play out under the Junta would have to work, through marginalizing any opposition that would want to frame it as ideological and reframe it as a sectarian conflict that ultimately would be damaging to the Junta in the long run. In that light, it could therefore be easy to square with what happens ITTL with the British version of 23-F, where Protestant militias take over the provincial government in Belfast alongside the military occupation of Northern Ireland, leading to protests and riots in Catholic neighborhoods in response. Ultimately, though, much of it hinges on keeping a clamp on butterflies in NI by having the OTL narrative conform to the whims and needs of the Junta.
But yes I didn't mean to imply Northern Ireland is exactly the same, and indeed the troubles played out very differently to OTL, with political violence spreading across community lines. I meant in broad terms Northern Ireland isn't as different to OTL as Scotland is - with the main themes of the TL, political violence, party fragmentation and the peaceful democratic transition process all having occurred in OTL Northern Ireland.
But for the sake of brevity I have decided to focus on GB because a detailed dive around Junta/Transition Northern Ireland would be an entire TL in and of itself. If anyone else would like to write that I would be delighted to see it, but I unfortunately don't have the NI knowledge to do such a complicated TL justice!