I am always very wary of equating Jean/Jane with Janet. I know the LDS think they are interchangeable, but I have only ever seen a couple of examples. I have many, many more examples of families who had a daughter Jean/Jane and a daughter Janet, so clearly thought of Jean/Jane as a separate name from Janet. So I am not convinced that it happens often enough to be useful without additional evidence. Of course Jane/Jean and Janet both morph into Jeannie or Jenny, which may be the source of confusion.
On the other hand, Janet
is interchangable with Jessie. There is a birth of a Jessie Cunningham in Alloa on 11 July 1873, father William Cunningham, mother Margaret Reid. This couple also had two sons named William, one born 1866 and the other in 1870.
Also surprised that no-one has suggested Dunmore in the parish of Falkirk in Stirlingshire
http://www.geograph.org.uk/gridref/NS8989where there is a Dunmore Wood as well as the better known Pineapple
http://www.geograph.org.uk/gridref/NS8888I see that the 1911 census gives Janet's age as 36 and the 1901 says 26. This means that she is three times more likely to have been born in 1874 than in 1875.
It should be simple enough to find out the parentage of the William Cunningham in the 1901 snd 1911 censuses. He had a 22-year-old son John, born in Bathgate, and he and his wife had been married for 27 years. There can't be that many John Cunninghams born in Bathgate in 1888/9, and John's birth certificate will tell you Jane's maiden name and the exact date and place of William and Jane's marriage in 1883/4. The marriage certificate will tell you the names of William's parents.