I don’t think there is any such thing as "perfect" speaker placement as long as you have them in a room with people, furniture, and pets. However, any of the major speaker placement formulas may improve your set up just by (a) getting the speakers away from the walls, (b) introducing symmetry in the relationship between speakers, walls, and listening position, (c) ensuring that the speakers are not equally distant from boundaries in more than one dimension. Beyond that, I’m skeptical that there necessarily is anything dramatically better about one of these formulas than another (Rule of Thirds, 38%, Cardas, etc.)
I’ve found that the Allison Rule is more flexible than others w.r.t. furniture placement. The Allison Rule (as I understand it) depends on 3 measurements, namely height of the woofer off the floor, distance of speaker front face to front wall, and distance of speaker front face center to the side wall. It states that the middle of these distances should be the square root of the product of the least and the greatest of these distances. So I place my speakers about 4.5 feet in from the side walls; midpoint of the 2 woofers is about 2 feet high; the front face is about 3 feet out from the front wall. That is, 3 feet (the middle distance) is the square root of: 2 feet (the least distance) times 4.5 feet (the greatest distance). The point is to maximize the differences among these 3 measurements, within the constraints of room size and speaker placement, in order to minimize room effects.
By "back wall", the OP seems to be referring to what other audiophiles usually call the "front wall", that is, the wall directly in front of the listener (and behind the speakers). In my experience, placing speakers very close to that wall may improve bass extension, but generally is not so good for imaging/soundstage. I prefer to pull speakers away from the walls and increase bass extension by adding a subwoofer. Also, I use highly directive (focused) monopole, sealed, hybrid electrostatic speakers. These tend to minimize room effects. I get a very sharply focused center image along with a rather flat frequency response between about 10hZ and 15kHz+, without any room treatments (other than furnishings) or PEQ. Then, to widen/deepen the soundstage, I use BACCH4Mac software.
I’ve found that the Allison Rule is more flexible than others w.r.t. furniture placement. The Allison Rule (as I understand it) depends on 3 measurements, namely height of the woofer off the floor, distance of speaker front face to front wall, and distance of speaker front face center to the side wall. It states that the middle of these distances should be the square root of the product of the least and the greatest of these distances. So I place my speakers about 4.5 feet in from the side walls; midpoint of the 2 woofers is about 2 feet high; the front face is about 3 feet out from the front wall. That is, 3 feet (the middle distance) is the square root of: 2 feet (the least distance) times 4.5 feet (the greatest distance). The point is to maximize the differences among these 3 measurements, within the constraints of room size and speaker placement, in order to minimize room effects.
By "back wall", the OP seems to be referring to what other audiophiles usually call the "front wall", that is, the wall directly in front of the listener (and behind the speakers). In my experience, placing speakers very close to that wall may improve bass extension, but generally is not so good for imaging/soundstage. I prefer to pull speakers away from the walls and increase bass extension by adding a subwoofer. Also, I use highly directive (focused) monopole, sealed, hybrid electrostatic speakers. These tend to minimize room effects. I get a very sharply focused center image along with a rather flat frequency response between about 10hZ and 15kHz+, without any room treatments (other than furnishings) or PEQ. Then, to widen/deepen the soundstage, I use BACCH4Mac software.