Andrew,
Some of the chronology seems a little suspect here. You say that John Riddell was born c 1650, the son of someone who had been granted lands by King William III in return for military service. The snag is that William III himself was only born in 1650, and didn’t set foot in England till 1688. He then had a military campaign in England & Ireland until 1692. So, if they were in Donegal pre 1650, there’s no way the Riddell family got their lands from King William III. He wasn't born.
Large numbers of Scottish & English (and some Welsh) settled in Donegal in the period 1610 - 1625 as part of the Plantation of Ulster (a settlement scheme devised by King James I). That’s perhaps a more likely time and reason for their arrival. Against that is the fact that there are no Riddells listed in Co Donegal in the Muster Rolls c 1630, suggesting a later arrival. (The Muster Rolls only list 1 Riddell household in Ulster at that period. That was a John Riddell who lived on the Earl of Antrim’s estate in the Barony of Dunluce, in Co. Antrim. Likely from or descended from a Riddell family who originated on the MacDonald estates in Scotland).
MacLysaght’s “The Surnames of Ireland” simply says of Riddell: “An English name numerous in Ulster.”
I looked in the 1901 census of Co. Donegal. There were only 3 households with Riddell/Riddles. All were born in Scotland, England or Co Tyrone & Fermanagh, so no obvious longer term connection with Donegal.
The tithe applotment records for 1827 list a single Riddell in the county. He/she farmed in Donagh town, Donagh parish. (That’s on the Inishowen peninsula, some distance from Raymoghy).
Griffiths Valuation (1858) listed just 1 Riddell in Co Donegal. He was James Riddell who lived in the town of Raphoe.
So there do not appear to have been many Riddells in the county in the 1800s.
Raymoghy has no church records for the 1600 or 1700s so it won’t be possible to check them. (The earliest church records for the parish start in the mid 1800s). Very few records exist for Co Donegal in the 1600s and 1700s generally and so researching that period can be very challenging.