Well, if your axes were aligned with the model axes while the geometry is angled, it would look like you are making the opposite side of the room. You could also select more than one group so you are flipping along the model axes instead of the group’s axes.
Here I exploded the group and remade it so its axes are aligned with the model axes. Note the huge bounding box.
Here I’ve selected two groups so the Flip Along is relative to the model axes, not a group’s axes.
You could also flip ungrouped geometry but it’s kind of dumb to explode a group for this and then remake the group.