The reason I mentioned the two different inputs to TV was that it rung a bell to something I had with my own set-up years ago. The TV was receiving signals from both a loop-through of the roof aerial (coming in via a satellite box and distribution amplifier) and the AV connections (SCART/RCA). This gave the ghosting you describe.
I went through the measures you are trying to no avail. Then, while I was watching a program that came via the television AV sockets, I just happened to unplug the aerial lead that arrived via the amplifier and box. The ghost images of people wandering around in the background disappeared.
I think I overcame the problem by putting an attenuator in the aerial lead. This cut the RF signal from the aerial system down enough to stop it interfering with the AV signal coming from the satellite receiver. In the end. I put the trouble down to being something to do with the TV. Perhaps there was a way that signals arriving into the TV from two sources could interfere with each other, even though that shouldn't really happen because only one or the other is selected at any one time.
Anyway, that's why the situation you have rung a bell and probably why I got the wrong end of the stick

Lets try a different theory. It is possible that something called cross-modulation is occurring. This can happen if the signal is
too strong. You could try cutting the signal down a bit to see what happens. This can be quickly tried by pulling the coax connector out of the back of the TV and holding it very near (almost touching) the socket. See if that has any bearing on the ghost images. Try holding the plug at marginally different distances, just to give an idea of whether cutting the signal strength down a little might provide a cure. If you feel that does help, it is possible to get a device called an attenuator to use in series with the coax lead. They come in various strengths and are measured in dB's (decibels). Something like a 3 or 6dB attenuator might be needed if this is where the problem lies.
It could be that the signal needs reducing where it comes into the house. In this case, it would be a job for the cable company.
It's all a hit and miss I'm afraid and the advice may not be on the mark. However, it is something that can be looked into.
EDIT: Are you able to link your cable box up to the TV using audio/video leads only (RCA)? This way, the only coax connection is to the cable box. The signal is then fed to the TV by way of the AV leads. You just select AV on your TV (if detection isn't automatic). I wonder what would happen under those circumstances.