Thomas Savory, maybe an immigrant?

This is more of a plea for help than a blog post, actually.  I've had such difficulty in pinning this man down that about all I can write about him will be theories and speculation.  The one thing I am reasonably certain of is that he married Mary (Marie) Woodcock (Woororke, or something similar) on January 26, 1595 in Hannington, Wiltshire, England.  This would probably make his birth date sometime in the early 1570's but that is really just a guess.  I show on my tree that his parents were Robert and Joan Savory, but I haven't seen good documentation for that and so I regard it merely as speculation.  Robert and Joan did have a child named Thomas in that time period and location, but so did at least one other couple, so I say "show me".

We don't know when he came to America.  In fact, there are those who don't think he came to America at all.  Because his daughter was Elizabeth Savory who married Samuel Eddy in Massachusetts Bay Colony, I lean toward the idea that he was here but I have no proof.  He most likely is not the Thomas who came to America in 1633, and neither is he the one who came on the Mary and John in 1634. 

There is even considerable dispute about his children.  Some lists do not include Elizabeth, but she does seem to fit in this family, due to her birth date of May 1607, between two of her brothers.  It's possible that Elizabeth came to America without her parents, but no proof has been found. 

So Thomas is a mystery, and I'm asking for help in finding him.  If he came to America, he deserves recognition.  If he didn't come to America, then how did Elizabeth get here, and were Thomas and Mary her parents? 

This blog post is written as quite evident proof that there is much more to be learn about our ancestors.  Did Thomas come to America and possibly live just a short time?  Did he stay in England and perhaps perish in the Civil War there?  Did he die on board ship?  How did he stay under the radar for so long?  I hope to update this blog post at some point in the future, but let this be evidence that finding accurate information about our ancestors is difficult!

The (supposed) line of descent is:

Thomas Savory-Mary Woodcocke
Elizabeth Savory-Samuel Eddy
Zechariah Eddy-Alice Paddock
Zechariah Eddy-Anphillis Smith
Elisha Eddy-Sarah Phettiplace
Enos Eddy-Sarah Brown
Enos Eddy-Deborah Paine
Joseph Brown Eddy-Susan Lamphire
Susan Eddy-Hiram Stanard
Louis Stanard-Mary Alice Hetrick
Etta Stanard-Loren Holbrook
Gladys Holbrook-Richard Allen
Their descendants