After the reformation the country was definitively crippled politically. To paraphrase Joseph Stalin, it was the Balkans in one country.
1172 was the great opportunity for England -- Henry II's conquest was facile, but more to the point, he achieved works in a few years that wouldn't be replicated for centuries. The pro-Rome faction of the church was quite powerful politically and crucially had all the skills he needed to fill out the ranks of his administration. It must be asked where he might find the money to conquer the country in detail -- the people deputised this task, the de Burghs, de Clare's etc. often cut costs by relying on local vassals -- but it would certainly have been both cheaper and more rewarding at that time than later.
(In fact even after Cromwell, the principle tenants on a lot of estates were Irish, and this was the class people like Peter Lacy, or Ambrosio (Ambrose) O'Higgins were drawn from after the post-1691 exodus... And O'Higgins purposefully chose to send his son Bernardo to an English protestant school.)
The window of opportunity was still open in John Lackland's time. He was uniquely lucky in that unlike Strongbow or de Courcy, he had the blessing of the King, his father. Anyone looking for a blood and gore horror story should so a King John of Ireland TL. Once the Irish aristocracy were totally obliterated, they would have re-emerged within a generation or two exactly as the English did under the Angevins. That would have been dramatically different from Irish history as occurred historically.
English domination of "the Isles" as a lot of Europeans call them would have been a huge challenge in those circumstances. No England as a mercantile naval power means no subsidies for continental allies, no balance of power and imaginably even a new empire in Europe, in which eventuality I'd probably be posting you this by pack mule rather than typing it on a computer.
Surrender and regrant could have been pursued at almost any time instead of getting it mixed up with the reformation. Even so, when capable, adaptable people like St Leger were in charge it was quite successful. The truth is that hanging the underlings was always one of the chief responsibilities of any English lord and the Irish Barons did not rely on the affection or loyalty of most of their tenants (whom they regarded with contempt; compare the very small number of names from the list linked to that are associated in any way with either the Irish lords or their Gallowglass retainers). A figure like St Leger could have worked wonders in 1250-1350 with even modest resources.
The problem is that there were always cranks waiting in the wings in London convinced that they could sort things out with a few hangings once the namby-pamby St Legers were out of the way. Cretins like Edward Bellingham could ruin years of patient work in an afternoon.
Pure conquest after Henry II's time would have been much more difficult whoever was in charge. There was raw hatred between city and country, and between the endless lists of feuding rulers in the countryside. Some, like the O'Byrnes and O'Tooles could hardly have been fully reformed simply because they had greatly enjoyed consequence-free banditry for generations.
If you look at the political and military situation of someone like the Gearóid Mór FitzGerald, you discover a picture as intricate and challenging as any. He was well aware that any idea of a surge of national patriotism propelling him to leadership of a united country was a fantasy. His friends as well as his rivals and enemies would have turned on him if they thought they would lose their privileges. "Disunity" as it came later to be styled was something highly desirable to most landholders in 14th-16th Century Ireland.
So it would have been difficult for England and very difficult for any Irish ruler to unite the country by force after 1200 or so. Saxon England gave the Normans a bloody fight even after having fought another hard battle just a few weeks earlier and then going on a forced march south, but was then conquered in a generation. The Danes likewise conquered half the country even though the English opposition was equally powerful then. And neither the Vikings nor the English succeeded in replicating these achievements in Ireland even though their armies didn't face opposition remotely as powerful there. This wasn't by accident.
But much of this was down to the peculiar expense of raising English armies. Had it been the Czar that was on the doorstep, more interested in glory and national power and less interested in money, the whole business would have been brief -- exactly as happened in many European countries countless times.