Richard
With DNA testing you could potentially get clues to the biological surname of your great-grandfather but to do this you need to test with Family Tree DNA who are the only company who have a Y-DNA matching database. If you are lucky you might match with someone who has the surname of your ancestor.
S116 is an alternative and less common name for P312 which is the most common branch of R1b in Britain. We can't say it's associated with the Beaker People because we are mainly testing the DNA of living people and you need ancient DNA to determine the past distributions. They might be very different from what we find today. There is a large P312 and subclades project at FTDNA:
https://www.familytreedna.com/groups/r-p312/about/background There's also a link at the bottom of that page to a P312 mailing list.
There is some information in the DNA section of the DFHS website about the different tests and how they work:
http://www.devonfhs.org.uk/devon-dna.htm Do have a look at the Devon DNA Project website:
https://www.familytreedna.com/groups/devon/about/background FTDNA have a sale on at the moment so it would be a good time to get tested. You might also like to consider the Family Finder test which gives you matches with genetic cousins on all your family lines and could potentially help to solve the mystery in the long term.