Hi caza
it's true ...this could be like finding a needle in a haystack......but I will have another go for you when I get an opportunity ! I have a whole list of look ups and only go to the WYAS once a week.
In Armley alone there are numerous possibilities......
Armley Baptist, Weslyan, Bethesda, Christ Church (Upper Armley), Whingate Weslyan (Upper Armley), United Methodist Free Church, Southfield Primitive Methodist,....... all with christenings in the 1870-80's.
St Dunstan, St Hugh, Oak Road Congregational, & Providence Chapel were all consecrated after 1884. Ven. Bede was not opened until the end of the 1930's.
There is an entry for an Arthur Ellis on the LDS family search website - in an ancestral file - (I know they can be dodgy!) - but this gives this 'Arthur Ellis' as born around 1875 - in Farsley - and also there is a similar entry in the IGI section saying Armley 1875. It gives no parent - so gets you no further !!
I will try to check off the above churches week by week - but it is possible that they were never baptised ! I will start with Christ Church - which was consecrated in 1867 and a new parish formed at the time - so it is possible that she decided to go to the new church.