I also don't have access to Lebor Eoghanach ( The book of Owens people ), but I have some info from it. I would love to get hold of it.
Regarding when or from where the break came, could drive you mad. There were so many O'Neill's rising and falling in the struggle with the MacLoughlinns between Aodh Athlamh d 1033 to Donal O'Neill d 1322, its hard to keep up with it all, I will have to sit down and study this 300 year period when I have time.
But something that caught my eye was, In or around 1088 a battle took place in Sithbhe, now called Sivey in County Tyrone. Donal Prince of Aileach and of Ulster was overthrown by his brother Hugh. In the same year and probably in the same battle Donal's kinsman Flaherty - Lord of Tullyhogue, was mortally wounded.
Now it says that this Flaherty was succeeded by Conor O'Brien, grandson of King Brian Boru. Only two of Brian's sons left issue, according to O'Curry ( Lectures ), namely, Tiege, and Donogh, who died in Rome. Conor, who was apparently a son of the latter, was driven from Munster by Tirlo, son of Tiege, when he took refuge in Ulster with the Cenel Eoghan, by whom he was honourably received, and now installed in the Lordship of Tullyhogue, a distinction only conferred on members of the royal family, or royal heirs of Aileach.
Conor, Lord of Tullyhogue, and "heir of Ireland" died in 1078, when according to the Annals of Inisfallen, his brother Kennedy was installed in his place. This very much places non O'Neills at the very center of things in Tyrone ?
Since DNA was the thing that brought this to light, surely it must be the thing to solve the mystery, you would think at some later date, they will find a group that match or come close to the O'Neill verity ?.
anyway I'm of to Ireland in the morning for a few days. I will be attending my nephews wedding in a small village in Tyrone where there are so many O'Neills they all have nicknames, I will be spreading the word lol.