Right so this isn't my patch (I'm over in Wiltshire, UK) but big cat sightings near the Appalachians have been on my radar for years. We get the same thing here on Salisbury Plain - large black cats that officially don't exist, witnesses who get laughed at, zero official acknowledgement.
The detail that always stands out in these American reports is the size comparison people give. When someone says "bigger than my Labrador and moving wrong" that's not a misidentified house cat or even a bobcat. That's something else entirely.
What I'd want to know is - did it have a long tail? That's the question that matters. A long heavy tail rules out most of the usual "you imagined it" explanations the sceptics love to throw at witnesses.
Anyone got photos or even just a rough location on the parkway? These sightings cluster geographically and if we can map a few data points it actually starts to tell a story. Post what you've got, doesn't matter how small the detail seems.