almost all of those movie methods involve streaming the video via wifi or what have you, which you wouldn't be able to stream to the tv while those are happening. If you have a method to pre-download the movie rental, such that some services offer for when you want to watch them on a plane, then by locating the file on your phone, you could use a smart tv's built in browser in conjunction with the WiFi Explorer app to play the movie on said tv on the same wifi network. That's the most sure fire way I know.
if the predownload is possible and you have a Samsung tv, you could use all-share to do the same thing, and it would run a lot better