Jon, I think you and I are operating with essentially the same sources. My hunch is that there was no second Joseph Ring in VA, and that the slight discrepancy in dates is due to the uncertainty and frequent sloppiness of much genealogical work. It would be a giant coincidence if TWO Joseph Rings from England both went to VA and both died there in the same year, 1703. There seems to be some disagreement about the birth year of Joseph, and I'm going with the data from his gravestone, which comes out to a birth in either 1646 or 1647.
The life span of his first born son, Joseph, Jr. is very doubtful (which you also indicate with your question mark). 1690-1796 is theoretically possible but so unlikely that I suspect there may be a transcription error here, and he may have actually died in 1696. Is there evidence that he was alive as an adult in the 1700s? Without delving back into my packed-away archives, my memory is fuzzy on this.
As for the possibility that Thomas Ring (born 1700) may have been a descendant of either Robert or Benjamin Ring -- Robert Ring's lineage has been thoroughly studied (that is my line) and there is no sign of any Thomas. Of course there may be an unrecorded birth yet to be discovered, but it seems doubtful. Thomas is not a name which appears much among the Rings of New England. My own database of this line (which of course is not complete) does not contain even one instance of a Thomas Ring.
If someone wants to pursue this line of investigation, and can gain access to British records, I would suggest starting with Benjamin. Almost nothing is currently known about him, and this would be a fruitful new area to open.
By the way, you give Joanne Rolfe (wife of Richard and mother of Joseph Ring of VA) as born in Melchett Park, Wiltshire. My record gives her birth in Whiteparish, Wiltshire. Could this be the same place, with two names? What is the source of your info?
Franz Martin