Regarding the spelling, I recently bought the book "John Howland of the Mayflower" Vol 1 - The First Five Generations Documented Descendants Through his first child Desire Howland and her husband Captain John Gorham", by Elizabeth Pearson White, copyright 1990, 2014 edition.
On pages 2 and 3 the marriage of John Howland and Elizabeth Tilley, with her parents, is written "Tilley". There is a long list of people who assisted with the book, all members of the Mayflower Society. The Society's website spells the family name "Tilley" also.
So my conclusion is that Tilley is the preferred spelling. I thought you might like to know how I came to that conclusion.
Names from that era are tricky because names (and most words) were not standardized, and there are examples of the same name being spelled different ways in the same document.