Help me out here, Dale. My mind is reeling.
I have no problem with your theory that John Rice of Dedham was an illegitimate son of Perrott ap Rice. It hasn't been proven but, as Erica says, Perrott had other sons. Easy enough to find those descendants, test them, and compare their DNA to your line. It won't prove the story, but it would make it more credible, and give you a firm foundation to show that John Rice did not come from East Anglia.
Where I start balking is your account of "the Beatrice figure". William ap Rice was the son of David ap Rice and Alice (or Alson) Martin, the heiress of the Martins of Rickeston manor. She later married Thomas Bateman of Honeyborough.
In your story, if I'm understanding correctly, Alice Martin the wealthy heiress becomes a shadowy "Beatrice", a washer-woman impregnated by Henry VIII at the Field of the Cloth of Gold. Is that what you're saying?
David ap Rice who married the Martin heiress was an illegitimate son of the famous Sir Rhys ap Thomas, a Tudor cousin highly regarded by them. Sir Rhys was even a Garter knight, probably the most prestigious honor the English kings can bestow. But that's not Perrott's Tudor connection??
I refer you again to the article linked above.
http://welshjournals.llgc.org.uk/browse/viewpage/llgc-id:1041698/ll...
"Rickeston and Scotsborough: A Study in Family History" by Major Francis Jones, a Fellow of the Society of Antiquaries and Wales Herald Extraordinary (1966).
Francis Jones could be wrong about the details, of course. He might have been missing some information. But, the fact that he was an FSA means he was an eminent scholar. The fact that he was Wales Herald Extraordinary means that he was an officer of the Crown, part of the English College of Arms, a professional genealogist with specialized knowledge of coats of arms and noble genealogies.
The line as it appears on Geni does not match the known facts, which might be contributing in some part to the confusion. Geni does not properly identify Alice Martin. And, it shows her son William as born 1500 instead of the 1521 necessary for your chronology. It shows "Beatrice" born about 1470, which seems to be accurate for Alice Martin (who married David ap Rice about 1490), but in your chronology that would make her 51 when William was born -- rather an aged washer woman, and perhaps not quite as comely in 1520 as she once was.
Another problem is that you have taken the historic William ap Rice and given him the additional name Henry. This would be a remarkable historic find, because the English and Welsh of this time did not yet use two given names. The practice began, haltingly, later, in Elizabethan times. I do seem to remember that there is one instance this early, or maybe almost this early, but it was litigated through the ecclesiastical courts and determined to be not allowed.
I suspect you might be adding the name Henry so you can identify him with a different man. I suspect a Henry Rice who received some kind of pomegranate arms from Queen Mary.
I'd be interested in the details of this award by Queen Mary, but I think you might be over reading the evidence. It is an old heraldic practice for kings to grant some part of their arms or one of their badges as a heraldic augmentation to people they wanted to particularly honor. Rarely does it mean there was a blood relationship. The Spanish kings granted a pomegranate augmentation to men who particularly helped with the conquest of Granada. It wouldn't be too much of a stretch to think that Mary would use it to honor men who helped in a similar "crusade" against the Protestants.
Lots of confusion to clear up.