Did a quick web search on the person with no results. For a serious search on this Thomas More I can point you, if so interested, to an excellent professional researcher who I highly recommend and who might be able to assist: http://annmcrodenmensch.webs.com/http://annmcrodenmensch.webs.com/ https://sites.google.com/site/annmcrodenmensch/ Ann's resume speaks for itself.
Regarding Richard More, I am a compiler of his new Wikipedia article and am a descendant, so have spent years on his fascinating ancestry. About the Thomas More mentioned, there is a possibilty he was a descendant of one of Richard's sons, although I have not traced their descendants. My ancestor is Richard's daughter Susanna, who is his only child known to have descendants alive today. Richard's new Wikipedia article: http://en.wikipedia.org/wiki/Richard_More_(Mayflower_passengerhttp://en.wikipedia.org/wiki/Richard_More_(Mayflower_passenger)