Sandwich, but which county of England?

Thomas Dewey, The Settler is often referred to as having emigrated from (or born in) Sandwich in the county of Kent. However, it is difficult to find hard evidence that Sandwich in Kent was the right Sandwich.  If Thomas had any connection at all with Sandwich, I believe it is far more likely that Thomas may have resided in the place now known as Swanage in the county of Dorset. This hypothesis is based on evidence detailed below.

 1. Old Maps:
During the 1600s, Swanage in the county of Dorset was known as Sandwich. This is shown on a number of maps, a good example is Morden 1695 of SE Dorset http://www.dorsetshire.com/old/mapindex.html which shows modern day Swanage as Sandwich, as well as showing Sandwich Bay next to Poole Harbour.

Another example is {BleauMap6} Bleau's map of Dorset, 1645 which shows the place 'Sandwiche' and 'Sandwich Baye' just to the south of Poole harbour.

 2. Official Documents:
There are references within several official documents of the time, for example:-
PROB 11/125/38:
Thomas Abbot, Yeoman of Ulway, Swanwich, Isle of Purbeck, Dorset
Dated: 20 March 1614/1615 (taken down by word of mouth in presence of Brewen Cockeram, Clerk of Sandwich and Lewes Cockeram, Yeoman of Sandwich 11 April 1615).
 
 3. Winthrop Connection:
Swanage in Dorset, England is only about 25 miles from Dorchester (the County Town of Dorset) and about 10 miles from Wareham, Dorset, both of which are associated with Winthrop settlers.

 4. Protestant Links:
Swanage is just south of Poole, which was a puritan stronghold during the English Civil War (http://en.wikipedia.org/wiki/History_of_Poole).

 5. America Link:
The town of Sandwich, MA, USA (according to {GlassMuseum}, "Incorporated in 1637, Sandwich is the oldest town on Cape Cod") is about 10 miles from the town of Wareham, MA and about 40 miles from Dorchester, MA.  The similarity in geographical layout between these 3 towns in Dorset and towns of the same name in MA is unlikely to be just a coincidence.  This strongly suggests that in 1637 the early settlers coming from the county of Dorset referred to the town in England that is now called Swanage, as Sandwich.

 6. Later Name Change:
Around the end of the 1800s, when books on Dewey Family History were being published, Sandwich, Dorset had already started to be referred to as Swanage, for example the Archer map of 1860, http://www.dorsetshire.com/old/mapindex.html.

 7. Fishing Industry
Poole and Sandwich (now Swanage) in Dorset had a thriving industry based on Newfoundland cod fishing; Sandwich in Kent was already a port in decline. It is possible that Thomas was involved with the fishing industry before deciding to settle in America, which could possibly explain why he does not appear on any 'passenger lists'.

 8. Distribution of Dewey Surname:
In various records (e.g. census records) there are a large number of references in the past to the name Dewey and its variants in the counties of Dorset and Wiltshire; there are very few such references to Dewey in the county of Kent.