Have you considered an NPE sometime prior to 1580? Where was this earliest known Oates from? Were there Keigs about?

Here are the two Otes given names Frances mentioned:

1511 - From Otes McTagart 6d. and William Lyst 12d. for 1 chamber demised as above / Conchan Cottages
1511 - From Otes McTagart for the mill of Doway demised to him as above / Braddan Farm of Mills