Just to recap - Your Elizabeth Cavendish (nee Moore) was d/oThomas Moore & Eleanor Kneen & my William Moore was s/o these parents. Eleanor Kneen I have as chr 1796/7 in Patrick, & possible burial March 1862 aged 69. Peel. Maybe that is why her husband went back over to the west of the island from the south . The following is what I have on Thomas Moore chr Jan. 1785. 2 sisters, Jane Nov 1787 & Isabel Aug 1792 all in Arbory to parents Thomas Moore c 1759 & Mary Cashin born maybe May 1761 Rushen. I have a marriage for these possible parents in Rushen January 1784. Witnesses Henry Lowey, ev Qualtrough. Possible parents of Mary Cashin (1761 Rushen) are William Cashin & Isabel Lowey (Lowee) married in Rushen May 1746. Three chn namely Mary 1761, Eleanor 1758 & John 1754 all in Rushen. The Lowey surname crops up a few times.
Last year on the iomfhs message board I received some info on Henry Lowey & Isabel Moore. Also Taubmans - don't know if you can still find those messages.
Possible parents of the Thomas Moore who married Mary Cashin are John Moore & Catherine Taubman but these are not verified. Thomas Moore & Eleanor Kneen named their first children John, Thomas & Jane so there is a connection with names. It's a lot harder the further back you go isn't it ?