On the topic of Trewartha/Andrewartha etc- Laurie, who was one of the people who made the Mike Tree page, had this to say to me a few years back:
"A note on Roger Barkacke. When you have traced the TREWARTHAs back to the top of the tree you will find Roger BARKACKE or TREWARTHA or ANDREWARTHA, a somewhat shadowy figure.* He did exist at about the right time, but I am not sure that he is actually the proto-TREWARTHA. You may be puzzled about his multiple names unless you know a little about Cornish names. If you do know even a little about the subject don't bother to read on, as you know as much as I. ANDREWARTHA is the same as TREWARTHA with the addition of (I am told) a definite article. As a rule before the 20th century you do not find both names recorded in one place. Where families move to a place where the other form is current they appear with that name. Very occasionally a family member is recorded with the other form from the rest of his family. Whether this was by design or by the whim of the local vicar it is not possible to say. Roger had a grandson John TREWARTHA, whose son Philip ANDREWARTHA, born in 1642, was the progenitor of most of the existing ANDREWARTHAs, though, as I said, some may have picked up the name by moving into a TREWARTHA area. As Scottish crofters still are (I understand) Cornish farmers were known by the names of their farms. Roger would have farmed at Trewartha (the place at the top). The TREWARTHAS were "the folks who live on the hill". (One or two people Anglicised the name to UPTON.) Unfortunately the name is not unique and there is research as to where it was. Probably at St Agnes."
* Note that this is the guy that my cousins disagree about being the father of William. I haven't researched it and have no opinion either way.