The Protestant ruling class in Ireland became known as the Protestant Ascendancy and in the latter half of the 18th century many of them organized into the United Irishmen and voiced their displeasure with England with regard to trade, tariffs and many issues that placed them at a great disadvantage despite owning most of the property in Ireland. Many of these Protestants were part of the failed insurrection of 1798 against the British and they paid with their lives. Indeed Methodists were frequently in the forefront for Catholic emancipation then and also vocal for peace in the North of Ireland in the last 40 years.
To get beheaded in Ireland one had to commit an act of treason against England and to row to Scotland is surely an act of utter desperation, a 22 mile trip at the shortest point in very unfriendly water. I suspect that the four brothers plotted against the government in some way and paid the price as did Wolfe Tone, Lord Edward Fitzgerald and other Protestants some years later. Plotting against the Catholics, which would have gained nothing, might have earned praise from London at that time but that was not occurred.
Perhaps your scribe got the history a little mixed up. Incidentally, Connaught is a Province, not a parish.
Anyway, you have a most fascinating challenge and I wish you nothing but the best of good luck.