Good food for thought in these texts as well.
"Of this family which assumed their surname from the town of Ashburnham co Sussex was Piers lord of Ashburnham whose son Anchitel had a son Bertram who from king Harold was sheriff of Sussex Surrey and Kent and constable of Dover Castle which he defended against William the Conqueror Stephen de Ashburnham was a benefactor to Battle Abbey Reginald de Ashburnham held two knight's fees of John earl of Eu temp Henry II His descendant John Ashburnham was sheriff cos Surrey and Sussex 1401. "
Debrett's Peerage of England, Scotland, and Ireland. revised, corrected and continued by G.W. Collen, 1840
https://archive.org/stream/debrettspeerage08debrgoog#page/n98/mode/2up
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Jedburgh Estriels mis spelt it should be as it is in Duchesne's copy Escriols or Criol a name that appears again on the Roll in its Anglicized form of Kiriell It derived from Robert Count of Eu whose younger son Robert obtained from him Criol or Crieul near Eu He had been previously in possession of Criol as appears by one of his charters to the Abbey of Tre port Gall Christ xi col 13 Instr The Norman People In Domesday it is written Cruel Robertus Cruel held Esseborne Ashburnham in Sussex of his kinsman the Earl of Eu who then governed the Rape of Hastings and I think there can be no reasonable doubt that he was the progenitor of the Ashburnhams But they themselves claim a remoter ancestry My poor and plaine Pen writes Fuller with genuine enthusiasm is willing though unable to add any lustre to this Family of stupendous Antiquitie The chiefe of this name was Highe Sheriff of Sussex and Surrey anno 1066 when William Duke of Normandy invaded England to whom King Harold wrote to assemble the aw Comitatum to make effectual resistance against that Foreigner The Original hereof an honorable Heireloome worth as much as the Owners thereof would value it at was lately in the possession of this Familie a Familie wherein the Eminency hath equalled the Antiquity thereof having been Barons of England in the Reign of King Henry the Third There is certainly no record of any such barony and I fear King Harold's writ is not forthcoming either In point of fact this Saxon descent rests on the sole authority of Francis Thynne one of the inventive heralds of the time of Queen Elizabeth who tells us that Bertram Ashburnham a Baron of Kent was Constable of Dover Castle in 1066 which Bertram was beheaded by William the Conqueror because he did so valiantly defend the same against the Duke of Normandy There are however various difficulties to be met in this pedigree in addition to the historical fact that Dover Castle though styled the lock and key of the whole kingdom surrendered to the Conqueror without striking a blow Bertram's two sons Philip and Michael are said to have been also executed but his grandson Reginald reappears in possession of the estate as one of the benefactors of Battle Abbey Now the name of the Saxon owner of Ashburnham as given in Domesday was Sewardus and not Bertram and there is no evidence to show that the posterity of Robert de Cruel were ever dispossessed According to the common practice of those days they styled themselves De Ashburnham bearing their paternal name conjointly during five or six generations. Thus it seems evident that Reginald de Ashburnham who bestowed some lands and two salt works on the monks of La Bataille and his son Stephen who confirmed the gift and sold lands as Steven de Cuell to Robertsbridge Abbey Mon i 916 were in reality of the Norman race that received Ashburnham at the Conquest Their beautiful domain has been transmitted by direct male descent to the present Earls of Ashburnham who are probably though far from admitting the fact themselves the last remaining representatives of this great baronial house."
The Battle Abbey roll, with some account of the Norman lineages
Published 1889 by John Murray in London
https://archive.org/stream/battleabbeyrollw02battuoft#page/10/mode/2up
I think this reverts to a discussion of the accuracy and validity of the "Battle Abbey Roll".
"It is known to modern historians only from supposed 16th century copies of it published by Leland, Holinshed and Duchesne, all imperfect and corrupt. Holinshed's is much the fullest, but of its 629 names several are duplicates. The versions of Leland and Duchesne, though much shorter, each contain many names found in neither of the other lists.
Several names on the role are disputed; Camden, as did Dugdale after him, held them to have been interpolated at various times by the monks, "not without their own advantage." Later writers went further, Sir Egerton Brydges denounced the roll as "a disgusting forgery," and E.A. Freeman dismissed it as "a transparent fiction."[1]" -- http://en.wikipedia.org/wiki/Battle_Abbey_Roll
"There exists a copy of the Battle Abbey Roll which predates Leland's supposed copy by two centuries, which was not apparently known to the Victorian antiquarians. It forms one section (folios 105v-107r) of the mid-14th-century manuscript known as the Auchinleck manuscript,[3] one of the greatest treasures of the National Library of Scotland. Produced in London in the 1330s, it acquired its name from its first known owner Alexander Boswell, Lord Auchinleck, who discovered the manuscript in 1740 and donated it to the precursor of the National Library in 1744. A comparison of the list of family names in the Auchinleck version of the Battle Abbey Roll with other extant lists appears as yet unperformed." -- ibid.
I looked it up - it can be found online - and it *is* just a list of family names, some recognizable, some not.
The short of it is, the various compilations may not record persons or families who were actually present at Hastings, but may well include those who came over later to assist in the "pacification" of England.
Such wonderful citations and concise quotes, and so refreshing to see how you've traced each idea about these names back as close to its origin as you're able. The time you take to share what you've learned in this approachable format will give a balanced perspective on what we know about these names to a great many people.