Mendax Murder Method

This theory details the method Benjamin Mendax used to murder Kathryn Davies. It assumes that Kathryn Davies did, in fact die, although it may potentially be altered so that she's just unconscious and not dead.

The Easy Way
The obvious, easy way to kill Kathryn would be to simply walk into her flat at 10:15AM and shoot her. This is what the prosecution would have us believe Richard Kingsley did for most of the trial.

Why this is wrong

 * Why didn't anyone hear the gunshot?
 * The trailer briefly shows security footage of Mendax entering what's likely Kathryn's flat. Both of his hands are empty and there doesn't seem to be anything he can use to conceal a gun. This is most likely the only time he's seen entering the flat. If it turned out he entered before with a gun, that would be a Turnabout for Tomorrow tier trick.
 * It doesn't explain the final contradiction, specifically that there's no blood splatter on the walls.

The Right Way
Given the existence of the security footage, the prosecution was probably not aware that Kathryn Davies left her apartment. This raises the question of how she exited. As we only know of a camera outside her door, the only other possible exit is her window. For reasons unknown, Kathryn Davies opened her window, tied a long piece of rope to a piece of furniture, and used it to climb down her apartment building. Her actions are suspicious but as long as she has a reason that's explained later, that does not debunk the theory. What she was doing could even be a part of Mendax's motive.

Kathryn was then murdered somewhere outside her apartment, likely near the Beefy Mare during Mendax's second break. Mendax loaded her corpse into a van and driven her over to her apartment, which is stated to be nearby. He climbed the rope into Kathryn's flat and opened the door from the inside. He could have even left the gun at this time but apparently opted not to. He then left the flat, tied the rope Kathryn used around her corpse and then went into the apartment building. Finally, he entered Kathryn's flat through the door he left ajar and pulled Kathryn's corpse into the room. That was when he called the police.

Why this is right

 * It explains why there was so little blood at the crime scene.
 * Kathryn's hand could have been broken when she jumped out her window.
 * It explains why nobody in the apartment heard a gunshot and why only Mendax found the body.
 * It explains how Mendax could have shot her despite the security footage not showing him with a gun.
 * It's more interesting than the wrong way.