I have usually found the DAR records more useful than the SAR records. But DAR only lists John Atkinson's descendants that have been proven and a son John is not one of them. I was hoping that you needed Johnston Co. info as so much of it is available on-line. It sounds like you need Roger's will and while looking at the Dinwiddie, Virginia collection in the Family History Library Catalog it looks like not much is available before 1830. The loose wills they have record of said pieces were missing etc.
However, have you used their microfilm of the Bristol Parish Register 1720-1794 and Vestry Book 1720-1789 FHL US/CAN Film  ? It states that Bristol Parish included Dinwiddie and Prince George counties. This might include birth and christening records. I have never found what I wanted in the VA parish registers I was looking at, but I thought if you were desparate you might give it a try. Sorry I couldn't be more help.