Hi,
I think Christopher may be right about it being Killyleagh.
There is a William Thompson signed the Ulster Covenant there in 1912, also an Elizabeth.
Then with the Finley signings [this spelling there aren't too many] there is one for Killyleagh, none other that may be suitable except a village in Donegal, Killea [?] that has a Finley.
As the family were supposed to be there in 1912 i would say Co Down is a better bet.
Possibly why no traces of them in Co Londonderry.
Regarding soldiers, no Martin Finley that would be suitable. Could only find one at all, joined Royal Irish Fusiliers in 1881.
Have quite a lot of 1st war military info for City and County Londonderry and found nothing.
There was a Norman Finley killed with the Canadians, more searching can see if this leads anywhere.
Canadian records are on-line. And as many Ulster families went to Canada would be worth a look.
See this lady is still using the boards so personnal message may bring her back here.
Rob