There are apparently several lines of Box families that may or may not be related.I believe the line of Robert Box born abt. 1734 goes back to Robert Box found in deeds in New Castle Co. Delaware in 1728-1730. There is also the line of Thomas Box and Samuel Box of North Carolina (1757) that later moves into South Carolina.There are indications this line is related to the line of Robert Box of Delaware but the connection is not known. There is also a line of Samuel Box (Revolutionary War soldier) who was born in 1745 in SC that is not the Samuel Box of North Carolina. And there is the family of Will Box in GA. The descendants of Will Box and descendants of Robert Box of Delaware both seem to be listed in the 1805 Georgia Lottery but I know of no other connection.
I am of the opinion that most Box famiies from South Carolina derive from the Robert Box of Delaware and it will be helpful to have DNA testing prove or disprove that.
I believe but cannot prove Linda's Jonathan would be a 1st cousin to Stephen Box, John Morris Box and Robert Box, Jr. sons of Robert Box b. 1734.
I would suggest you start a thread on Box DNA on the Box Genforum in a attempt to interest other lines inDNA testing.