All the Republican movement got out of the war was the end of absolute majoritarian rule and the recognition that their right to aspire to a united Ireland was legitimate, and not some treasonous conspiracy.

Not so. They got considerable reforms in admistrative, judicial, police, citizenship and various other matters, which set in motion the process of levelling the playing field. They also got the disarmament ant demobilization of their hard men, which must have been a relief for most...

The harvest was pretty rich. The question of whether the war brought it nearer is a complicated one. Imagine there had been no war : would such a deal have been possible on the UK side before the late 90s?

No Conservative PM would have been willing or capable of it... Um Wilson? Callaghan? They would have had to deal with anti-Catholic sentiment among working class British voters...

_{It is rightly acknowledged that people of faith have no monopoly of virtue - Queen Elizabeth II}