Julie, it has been a whlie since you posted this, so it may not be of interest, but I have a large data base on the family name and am familiar with your John TR Seagraves. If you are interested, I can share what I have with you.
On he subject of spelling variations, I once wrote a short article on the Genealogy.com site about the variations in the Seagraves spelling. The short summary is that spelling does not matter in this research. All of us with any variant of the name come from the same general source. Our ancestors were not paticularly concerned about or even aware of, in some cases, how their surname was spelled by clerks, census takers and other such scribes. Only in recent decades have we focused on that detail.
Be careful of the "facts" from Jerry W. Segroves. There is no source or reference describing the exact origin of our family name. Neither is there a source which shows a Thomas DeSegrave being part of William the Conqueror's army. He is mentioned in the Domeday Book compiled in 1086 as a landowner in Leicestershire. We do not have a source for any particular immigration from England or Ireland of an early Seagraves. There are three 'branches' of the family dating from colonial times: North Carolina, New Jersey and Massachusetts. Only the MA branch has a genealogy that describes the original family from England.
I have more if you are interested.