More information, still no evidence
An inquiry to the Nelson County Historical Society asking whether there had actually been a narrow gauge soapstone railroad found its way to an attorney named Dick Whitehead who sent me copies of ancient DGMR reports on Phoenix Stone Company.
DGMR ECON FILE - STANDARD SOAPSTONE CORP ca1926
The Phoenix Stone report mentioned that the narrow gauge ran to Arrington. So I collected my maps, gassed up the truck and headed out to Arrington and again came up empty. I saw nothing there to suggest an abandoned railroad grade or transfer point.

USGS Arrington quad

DGMR ECON FILE - STANDARD SOAPSTONE CORP ca1926
The Phoenix Stone report mentioned that the narrow gauge ran to Arrington. So I collected my maps, gassed up the truck and headed out to Arrington and again came up empty. I saw nothing there to suggest an abandoned railroad grade or transfer point.

USGS Arrington quad