Thanks, Helen, for bringing the profile of Fuller-7294 into the discussion. Darlisa, thank you for pursuing all leads in the quest for the origins of Fuller-117.
A good deal of the research on those two profiles (esp. Fuller-7294) is mine. I am convinced that the Norwich Matthew is _not_ the man who came to Plymouth (who is among my 8th great grandparents). The "Mathewe" who was married at Norwich in 1629 is far more likely to be one who remained in England, probably the same man who died at Strumpshaw -- within ten miles of Norwich -- in November of 1678. And he may also be the Matthew Fuller who was christened at Holt in 1594; Holt is a little further from Norwich (roughly 20 miles, as the crow flies, per Google Maps) than is Redenhall (about 15 miles), but those distances are certainly within the same general "range of usual mobility" for the time. I do acknowledge that the coincidence of two Matthews with fathers named Edward is most intriguing, but we would have to find some remarkable, additional record in order to prove that the father of Capt. Matthew Fuller had migrated all the way from his native Redenhall to Holt; by road, as George has indicated above, that would be an unusually long "remove" for those days... nearly twice the distance the proverbial crow would fly.
As indicated in the Research Notes section of Fuller-7294, it is a somewhat wistful coincidence that the Matthew whose death was recorded at Strumpshaw died within three months of Capt. Matthew Fuller's passing on the other side of the Atlantic.