I think this is a different Joseph Moorhouse, as my one was a farmer and I have his line going back to the early 17th Century. I will look at it to see whether there is a link anywhere to your Sarah Moorhouse.
Unfortunately, as we are pre-1837 birth and marriage certificates will be be available, only the PR's and BT's, so that is not an option.
One additional piece of Kaye information I have is that living with the couple in 1841 was a Joshua Kaye, whose age was given as 75. I suspect strongly that he is Easter's father. Have you come across a Joshua anywhere?