It doesn’t sound like your TV is having trouble handling the playback of large file sizes or any kind of buffering issue, but it does sound like there is a problem with the way it’s handling motion. There might be a some settings you can play with relating to the refresh rate. Or it might be trying to apply its own kind of ‘frame blending’ or smoothing. I have all ‘smoothing’ settings turned off my TV because I like that film ‘flicker’ you get when watching movies in the cinema. But when I go someone else’s place, they have screens which have the smoothing turned on, which is great for sports and games, but looks horrible when viewing films (I think). This video explains it in more detail- https://www.youtube.com/watch?v=acFRnyQ2rEQ.
In in all, it definitely sounds like a TV problem and not a codec issue. Do you get the same effect on other TV screens?