After speaking to the county archaeologist David Strachan, we came to the conclusion that the stone I found half-buried was probably the side-slab of one of the cists that was discovered “many years ago.” It was probably stood upright by workmen when the cist was ploughed open to mark the grave, and left standing since then. It doesn’t have the appearance of a standing stone, especially if that stone was supposed to have been the remains of a circle.
This doesn’t take away from the fact that there may well have been a stone circle on the site at some point, either around the cairn (long since ploughed away) or nearby.