Dust in Clean Out Box

Yes that can work as it will right in the corner in the stud bay to the left. You have the option of running the muffler box out towards the camera, down the wall or even across to the right. Depending what you perceive will be least intrusive. You could even try it with just the opening and see is the noise is or isn't bothersome. It it is then make the muffler box.

Yes there or in the first picture you put up. Your choice. You know what you plan on putting in that area so do what will fit the location best.