You can get the "The Tree and the Apple" and "Let Bygone Be Bygones" endings on the same playthrough, since they have exactly the same requirements. As soon as you trigger one ending and get the achievement for it, pause the game, quit to the main menu and select the continue button under the DLC. You will be back in the house and can go ahead and trigger the other ending. Basically, you only need to do two playthroughs of the DLC this way. It will save you a good amount of time. Note that I could get the true ending before the good or bad one, so I don't think there is any particular order in which you have to acquire them.
I recommend following this guide step-by-step:
It will get you all the achievements beside
Too Little, Too Late, for which you need to do another playthrough.
Warning: The video guide created by the user rus199410 for the collectibles of the DLC is missing one drawing, so you won't get the collectibles achievement following that one. User Beth Bear from the link I posted above has them all.