As the title says I think they should change the first grim location to remove the backtrack.
Backtracking is really irritating and brings the entire party to a screeching halt while you wait for one member to run all the way down the room and back up again.
From a difficulty perspective it makes sense to give the players the grim at the start of the barracks (one of the most difficult spots in the entire map) instead of at the end when you have already cleared your way through it. Fighting your way through the barracks against hordes and bosses while carrying the grim is how we have done it almost since launch and now that it has been changed it just feels wrong.
So either change the jump puzzle to involve obstacles on the first floor instead of having the players drop down from the second floor. Or alternately add some kind of one-way gate like a floor hatch that is barred from underneath that allows the player grabbing the tome to return to the second level.
Another idea which is less about the grim and more about the level itself would be to add a deployable ladder at the exit that the players can activate. This lets the person grabbing the grim have a shortcut back up and also prevents the players from having to repeat the room multiple times which can get frustrating and tedious, especially if you drop a boss on them.