Since this gen is the reboot for the series, they should do something radical for the Remakes of RSE as well. But I'm not sure what could be radical, but not TOO radical. I wouldn't want it to be TOO radical as I think things that would be considered TOO radical deserve to be on the main games of the gen instead of just on 'extra' games of the gen such as remakes.
For example, since in R&S you had to go to different towns/cities for Contests, why not have two stories to choose from, one being the normal 8 badge run and a new Pokemon Coordinator run. Of course, GF would need to move around the locations of the Contest Halls for it to work, plus come up with a slightly different story. Then, once you beat the different contests, you can compete in the Grand Festival (which would be in Ever Grande City). Once you beat either the E4 or the Grand Festival, you can do the other story (you will practically be starting over the game, but you will eventually be able to get the pokemon from your other story). After you beat the story, you can enter "free play" mode (which is what you are left with in the pokemon games of the past once you beat the main game), and have access to both the Pokemon from your Coordinator playthrough and the 8 badge run.