This seems a sticking point then: a majority of British voters have to be fine (or at least don;'tm consider it a dealbreaker) with withdrawing troops and Irish reunification, and in 1979. How do you get that? Something would need to happen in Heath's second term, either something to make people go "screw this" or "see, it's calmed down". (Or is actually calmer compared to OTL) What would that be?
Heath having a second term would probably provide fodder in of itself. Labour in 1974 walked into a minefield on Northern Ireland. Heath's Sunningdale Agreement had received pretty stern opposition from hard-line unionists in December 1973 but nothing prepared Harold Wilson for the UWC strike. The scale and organisation of the strike took the British totally by surprise - Wilson pondered withdrawal, he asked the Army about taking over essential services and 'clamping down' but they knew the Ulster police wouldn't play along and it would only escalate the situation. In the end he went with his gut and just tried to end the standoff, dropping Sunningdale, which was never his baby, and reimposing direct rule. After that Labour's NI policy was basically "keep the lid on".
If Heath is in power when the UWC strike happens, it could be something
very different. It's his baby on the line and he liked his decisive action. Some people did suggest plowing through the Unionist roadblocks and arresting the strike leaders straight away before the strike expanded and entrenched itself but again the Army weren't keen - during the strike soldiers at roadblocks were often little more than fifty yards away from armed paramilitaries on patrol. Also Heath despite his actions often being swift, he wasn't very good at timing and would probably be as confused as Wilson for the first crucial days.
Then the power goes out, the water stops running. Heath would want to intervene. Probably send some engineers to ensure the electricity, they'd be rejected by the strikers, then the engineers would come back with armed soldiers. Stand-off. Would he use force? Probably not, at least at first. The Army would be very loud by this point that they're not cool with all of this. A violent confrontation with the strikers will trigger attacks from the Unionist paramilitaries. The Ulster police will either join the strikes or 'return to barracks'. This would leave the British Army with a genuine occupation.
So what if Heath stays at stand-off and claims these extremists won't dictate the future of Northern Ireland? Then, the strike drags on for a long time. Despite the UWC having a fairly impressive organisation in terms of ensuring essentials for the local Protestants, there was plenty of shortages, seizures and worse. Sympathy will decline for the strikes if left alone but the political core would not be unbowed. I can see minor confrontations, soldiers removing roadblocks etc. definitely blood.
The need for supplies for the strikers would get worse. Probably raids to seize food stores and livestock from other areas (there were incidents of cattle rustling IOTL I believe). This is were 'containment' would probably lead to the most blood but also make the strike lose momentum. Again, the likes of Ian Paisley are not accepting Sunningdale in any form.
So either:
1) Drop Sunningdale, reimpose direct rule
2) Get stuck in, escalating things extremely
3) Talks
Heath would totally ignore 1, dabble in 2 until the RUC makes rumbles and then finally organise 3, which would probably lead to 1 with an empty agreement to continue discussions further. Regardless Heath isn't walking away like Wilson did even if he might have to eventually, leading probably to a few more weeks of striking at least, some blood and eventually a step down or muddled compromise that changes nothing.
Whether Heath goes for confrontation or containment with eventual talks, you'll probably see increased Unionist bombings outside of Ulster. In the Republic but also, depending on Wesminster's approach, possibly attacks on the mainland. Shooting the NI Secretary might seem crazy but if the Government is playing bolshy and insisting Sunningdale
will go through, it is far from impossible.
If unionists and soldiers are fighting on the streets, British ministers are dying and Protestant leaders are unrepentant, staying in Northern Ireland becomes a lot less attractive. Despite all the talk of the province being a legal part of the UK, if
both communities don't want you, why bother? This is where Benn could waltz in to cut the Gordian Knot.
From the chat of a lot of the Irish in recent months, I figure Ireland stays put: being in the EEC gives Ireland a better hand in dealings with Britain, and more so if they're in and we're out.
But is this in relation to the situation in 2019 or 1975? Back then the EEC was the CAP to Ireland and pretty much nothing else. There's a reason Ireland withdrew their EEC application after De Gaulle vetoed Britain's entry in the 1960s. Here you have much closer direct connections to the UK and weaker ones to the EEC. If things like the Sunningdale Mutiny happen as above, I can totally see Ireland sticking with the EEC but I've been trying to find info on Irish opinion of Britain's 1975 Referendum but have come up with nowt.