I've dealt with a newer hdr Sony, but I don't remember all the settings and terms. There are settings for something like cinemotion to mess with and maybe one called motionflow, that may be set too high for the cable signal. Also if there is a setting for live football or sports, change it to something like movie.
These TVs are so good these days that they can outperform the signals that they receive. Maybe try complaining to your cable provider, maybe there is an updated cable box or other improvements they can make. Also maybe the tech that comes out can help, they should have practice with this stuff.