I think I have the idea how the "restart" option works. Today I needed to kill Frigoris, the baron fallen captain you find while trying to reach Oryx's Sanctuary, but I had the checkpoint at the end before killing the big green knight, as always I tried to restart it, but it didn't work, then I thought: "what if... I press "X" (or Square for PS users) while selecting the level?", and voilà, I restarted the mission with the horoic modifier, I've just double checked it with my Warlock, but I'll triple check it later, 3 classes = 3 times the same quest. In short: To restart a mission with Heroic Modifier, press "X"/Square to restart the mission as usual, then while selecting the level, instead of pressing "A"/"X", press "X"/Square and you'll see the message to confirm you want to restart the mission. If it also works for you, then please spread this to other forums, posts, sites, places, whatever, and I hope Bungie fixes this already to only need to press "restart" once.