The man who arrived on the "Fortune" on November 11, 1621 originally appears on the passenger list as John Cannon.  It is not until later during the first land division of that his name appears as "John Carman", but even then not consistently -

"The Division of Land is recorded in Volume XII of the "Records of the Colony of New Plymouth", and reprinted in the "Mayflower Descendant", 1:227-230. Each family was given one acre per family member... The fales of their ground which came in the Fortune according as their lots were cast 1623. This ship came Novr1621.

these lye to the sea, eastward.

William Hilton 1
John Winslow 1
William Coner 1
John Adams 1
William Tench & John Cannon 2"

(John "Cannon" and William Tench are listed together as typed for whatever reasons unknown)

During the 1620's  John "Cannon" and William Tench seemed to have aligned themselves with John Billington of the Colony in a political controversy on how the Colony was to be governed.  In 1624, John Billington the Elder was implicated in the Oldham-Lyford scandal, in which blasphemous letters were secretly being written and sent to England trying to undermine the Plymouth Colony.  However, Billington claimed he was a scapegoat, and there was not enough evidence to show he was a party to the scandal so the matter was dropped. In 1630, John Billington the Elder was tried and executed for the murder of John Newcomen, whom Billington had shot with a musket in a quarrel over a past dispute between the two. He was found guilty by a grand and petty jury, "by plain and notorious evidence", and became the first Englishman to be hanged in New England.  Both John and Cannon/Carman and William Tench quit-deed there land to the widow Billington and that is the last they are herd of.

The history books record of John "Cannon/Carman" and William Tench that they "died or left the colony between 1623 and 1627." 

It was hard enough to survive within your own Colony then, no less trying to survive on your own for at least 4 years, if you believe this is the same man who moved later to Roxbury. And if he was when did he have time to meet his wife and have her come over in 1632?  They could have somehow gotten aboard a ship and returned to England only to come back over again, but where did they get the money for the expensive trip and do this man sound like a religious Puritan?