Dear John,
I have a quite a bit of information on the Bayntuns (being descended from Thomas Rolt, the eldest son Edward Rolt and Anne Bayntun).
I am intrigued that you say you might be descended from Edward through an illegitimate child. (I know that his son, the aforementioned Thomas had illegitimate children - but none them bore the name Rolt).
You also mention that Sir John Rolt bought bought the Miserden estate to "re-assert a link to the Bayntun / Rolt family". I unsure if this is so as neither the Bayntuns nor the Rolts owned property in Misserden - at least so far as I know. You may have found out otherwise...
As for Gerry Cullen's website it is shame that it has been taken down. However, much of the genealogical information should be treated with caution. This is especially true of the earliest Bayntun generations. A much more accurate pedigree is found in W.G. Davis,
The ancestry of Abel Lunt, 1769-1806, of Newbury, Massachusett (Anthoensen Press, 1963). Part of this pedigree can be found on this webiste which does a good job laying out some of earliest Bayntun generations:
https://sites.google.com/site/cochoit/family-articles/baynton.
I hope this helps,
F A C Rolt