I think the angle of the “contrail” is off from anything that would be flying. The head is moving mainly horizontal, and the tail is following at an angle downwards. How about a balloon/drone floating across and the string/tail hanging down but off to the side due to motion of the balloon. I can’t imagine a regular balloon - but a clear balloon trailing a large tail - made for the hoax. Or maybe like a weather balloon - but not sure it would have a broad tail like that.
Possible... the use of a telephoto lens can distort perspective though. Your guess/theory is a valid one.
My guess would be a lens artifact like a scratch.
This would be a fixed camera on a tripod. The moon would continue to move across the sky to the right making it appear as though the scratch is moving to the left.
The video editor zooms in and out on the artifact making it appear to move in relationship to the moon.