John,
Your research is approaching the dates when it gets very difficult in Ireland. You may come to a standstill. General advice on researching in this period can be found in Dr William Roulston?s excellent book: Researching Scots-Irish Ancestors, The essential Genealogical Guide to Early Modern Ulster 1600 -1 800. It will give you a list of suggestions.
The tithe records for that parish don?t appear to have survived.
You could try the Registry of Deeds records (Originals in Dublin, with a copy in PRONI in Belfast) for Killynure to see if any relevant leases etc were registered. (It wasn?t mandatory). These records started in 1708 and may name any relevant McClures, and sometimes their relationships to each other. Sometimes there are also references back to earlier leases and the persons named in them.
PRONI don?t appear to have any other documents in their on-line catalogue relating to Killynure & McClure. You could however try National Archives in Dublin.
I presume you have looked for relevant gravestones in the local churchyards. (Try Church of Ireland as well as Presbyterian as Presbyterians often used COI graveyards).
Search for any Encumbered Estates records on Killynure. These date to the 1850s, but often refer to 3 lives leases which can get you back into he 1700s. They are on fmp.
I looked at the Down Survey for 1630 but it doesn?t appear to have any relevant references to your townland.
Ayrshire seems a reasonable option for the family?s origins. Certainly many settlers did originate in that county. The Chief Undertakers in that part of Raphoe were Cunningham, Stewart (both from Ayrshire) as well Bishop Leslie and Knox. And obviously many of the original tenants came from their estates in Scotland.
Elwyn