I flew just north of GKT on our way home to BGF on Monday at that time. For what it's worth, I took this photo as we were passing TYS so I could work out another issue on the ground later. Clouds were present throughout the entire flight. We climbed through around MOR, bases starting around 5,500' MSL and tops at 7,000 MSL. I don't recall hearing Knoxville Approach talking to them, but they couldn't been on another frequency. I don't like to be a Monday-morning quarterback, but looking at this
track graph from Flightaware it appears that about 7 minutes or so before radar lost contact the aircraft entered a constant (not extreme) descent <position only flights must be enabled to view this track graph>. Purely a guess (and I will follow this and await the report because I fly through this area frequently), but based on my first hand observations of the weather in the vicinity at the time, it almost looks like he was VFR on top & descended through the cloud layer, probing, hoping to find the bottoms.