Thank you David, for wading into the morass of conflicting(?) snippets. Talking things through, with an open mind, is how unviable arrangements of the puzzle pieces get weeded out.
In a nutshell, Nathan Murphy's supposition that immigrant Edmund Kempe was the grandson of Robert Kempe of Gissing (er, which one -- there seem to have been two of them?) is based on the presumption that Edmund Kempe of Lancaster County, Virginia was the "nephew" mentioned in the will of Virginia Councilman Richard Kempe (which I have no reason to doubt, at least for the moment), together with the (groundless?) supposition that Richard Kempe was the same as the Richard Kempe who was the third son of Robert Kempe of Gissing. Where is the evidence for that supposition for the father of Richard Kempe? That is a critical question here -- and if we don't scare up some evidence, it seems that yet another gateway ancestor will also have to be detached.
Regarding the origin of Edmund Kempe of Lancaster County, there is one more clue: Widow Bridget Kempe gave a power of attorney in 1651 to Daniel Clark "of the Island of Virginia," per Virginia Colonial Abstracts, 2:182.
This Bridget would seem to be the widow of Edmund Kempe the weaver (the one who was not the son of Robert of Gissing -- at least not the son of one of the Robert Kempes of Gissing) -- and that is the Edmund Kempe that Richardson wrongly supposes to be the father of Edmund Kempe the immigrant.
You say that RJ Horace says that Edmund Kempe "seems to concede" the probability that Edmund Kempe the immigrant is the son of Robert Kempe of Gissing. But the problem is, RJ Horace's sources seem to show that there were two separate two separate Gissings and two separate Robert Kempes of Gissing (in two separate parishes) -- one of them with the Magna Carta lineage, and the other a son of John Kempe.
So who is who in this family? For starters, if immigrant Edmund is the son of Edmund the weaver and wife Bridget (who gave power of attorney in 1651), then he was NOT the son of the Robert with the known Magna Carta lineage. (Of course, maybe the other Robert -- if there were indeed two Roberts -- also has a Magna Carta lineage.)
Secondly, what reason is there to suppose that Richard Kempe was the son of one Robert Kempe and not the other Robert Kempe, or perhaps son of Robert Kempe's cousin Thomas Kempe, witness to the will of Robert's widow Dorothy?
To quote from Virginia Gleanings in England, p. 73: "While it seems practically certain that Richard Kemp, Secretary of State of Virginia, and his nephew Edmond Kemp, of Lancaster (afterward Middlesex) County, Virginia, were of the family Kemp, of Gissing or Gessing, absolute proof has not yet been produced.... Richard Kempe... died in 1656. In his will, proved in London, December 6, 1656... he makes bequests to his brother Edward and his nephew Edmond. The latter was apparently in Virginia. Edmond Kemp was J.P. for Lancaster County, Virginia in 1655. In 1656 he recorded a power of attorney for him from Sir Robert Kemp, Knight."
Sir Robert Kemp was the eldest son of the Robert Kempe with the Magna Carta lineage, so it seems clear that there is some sort of family connection to immigrant Edmund. But Douglas Richardson seems to have jumped to the groundless conclusion that Edmund Kemp was the nephew of Sir Richard and not, say, his first cousin once removed. (And if that sounds familiar, Richardson made exactly the same error in his broken Cudworth/Machell lineage.)
And with all that said, I'm going to further state that I haven't fully sorted out all the snippets that RJ Horace provided, so maybe I'm missing something here, and somebody else will see a convincing arrangement of the puzzle pieces, especially regarding the apparent two separate Robert Kempes of two separate Gissings.