This is a very unscientific answer to your question about the Pilkington/Pelkington difference.
The sound made made the letters "il" or "ill" are often pronounced by the Irish as "el" or "ell" - for example, if you listen to an Irishman describe someone as being "silly" he may often pronounce it as "selly". I could be quite wrong, but I believe this change in the vowel sound came to Ireland when many people from Yorkshire and other areas in England were sent over as military occupiers of Irish lands, or as Protestant farmers to counteract the Roman Catholic Irishmen. It is a working class pronunciation; the aristocracy or nobility who were often sent to take control of Irish lands and estates - or who built castles in Ireland in the 19th century - would not have used this dialect.
So, it makes complete sense that somewhere along the way, some of the PILkington folks were referred to as PELkington - or perhaps someone who was writing down what they said heard it as PEL instead of PIL - perhaps because they spoke in the same dialect.
This all goes to show that (and I say this as a former English teacher) we pay much more attention to "proper spelling" since the Victorian Age than people did before the 1800's. They wrote down what they thought they were hearing - which is why you get different spellings of the same name in the same documents. Keep in mind that most people were illiterate and they relied on somebody else to write down what they were saying.