Look at a maul and how it is used. A typical maul is about 3' long with a straight wooden handle and a 5 to 8 lb. iron or steel wedge shaped head on one end. If it were held by the end away from the head, there would be 24 foot pounds of torque to resist. That's a considerable amount and even someone with very very strong wrist is unlikely to be able to do it and couldn't swing it that way.
To overcome the forces working against him, a user starts a swing with one hand near the end away from the head and the other just below the head. He or she pulls the head close to the body, pushes up and lets the head fall forward while sliding the head hand towards the other. The head hand is pushing and the other is pulling and that leverage helps to accelerate the head along with the acceleration due to gravity. As the hands get closer together, the head reaches maximum acceleration just before impact.
The head stops relatively abruptly with a great deal of force since force = acceleration x mass and the acceleration which just took place over about 2-3 seconds has been decelerated in a tiny fraction of a second. At that point, the user is back to the position of having both hands at the end and being out of control of the other end. To make things worse, the users arms are extended and the wrists are rotated forward, putting him/her at maximum disadvantage in terms of leverage and the head may be stuck in something (use your imagination here). The complete cycle depends on how quickly the user can then move back into position to lift and swing again and the strength of the user and muscle fatigue have to be factored in. Most non-professionals can hardly repeatedly swing a 22oz. framing hammer with a handle length of 16-18" (just over 2 foot pounds of torque) and hitting nails even helps since the hammer bounces to some extent rather than being stuck.
I just don't think Sam had it in him to attack in the first round with a maul. I may well be proven to be wrong I know, but compare Sam to Kuriuz for example. Pixy noted that he is much more appealing than Sam. Part of that is no doubt his blue eyes, but his upright posture and broad round muscular shoulders are a significant part of it and they are in stark contrast to Sam's. The question of how long it took for Sam to lose his appeal upon arrival in Richmond was raised earlier and the general conclusion was that happened almost instantly. Not bathing probably played a role, but that immediate reaction is as much as anything related to body language and posture which are apparent even in the pictures the people making those comment have seen and been influenced by.
Sam may have had shackles on his feet when he made the walk up to the "Jesus told me to" comment, but regardless, just look at his body form, the way his legs move and his shoulders. He is neither strong nor fit, that shows over and over in photos of him, and makes sense for a kid who spends all of his time in a garage listening to awful music. I do however think he could do some serious damage with a ball-peen especially with too much caffeine surging through his system. I've got 4 different sizes in my basement right now, and I don't think anyone here would let me hit them in the head with the smallest. The ball-peen is close to the hatchet in form, grip, and size, and we know Sam had a thing for hatchets. Also, the maul is consistent if I read correctly. All victims were hit with the maul, but only Mr. Neiderbrock was killed with the chunk of wood? Please correct me if any reliable sources say otherwise. That leads me to believe that the maul was used in round 2 and not round 1. If the maul wasn't used on Mr. Neiderbrock, then that leads to a few other questions.
Sorry for such a long post, but I just wanted to make my reasoning clear whether it convinces anyone else or not.