Right click on Obduction in your Steam library and select properties > betas. From the drop down menu choose version 1.1 and let Steam download the old version.

You have to switch game version to 1.1 for the next step to work. This changes some small things, but has no effect on gameplay. Personally, I prefer this version, and you might as well.

Go to C:\Users\<your username>\AppData\Local\Obduction\Saved\Config\WindowsNoEditor and select Input.ini.

In Input.ini add the following:

[/script/engine.inputsettings]
AxisMappings=(AxisName="ConstantCursor_X",Key=Gamepad_RightX,Scale=15.000000)
AxisMappings=(AxisName="ConstantCursor_Y",Key=Gamepad_RightY,Scale=15.000000)
AxisMappings=(AxisName="Cursor_X",Key=MouseX,Scale=15.000000)
AxisMappings=(AxisName="Cursor_Y",Key=MouseY,Scale=-15.000000)
AxisMappings=(AxisName="LookUp",Key=Five,Scale=1.000000)
AxisMappings=(AxisName="LookUp",Key=Four,Scale=-1.000000)
AxisMappings=(AxisName="LookUp",Key=Gamepad_RightY,Scale=1.000000)
AxisMappings=(AxisName="LookUp",Key=MouseY,Scale=-1.000000)
AxisMappings=(AxisName="MoveForward",Key=Gamepad_LeftY,Scale=1.000000)
AxisMappings=(AxisName="MoveForward",Key=S,Scale=-2.000000)
AxisMappings=(AxisName="MoveForward",Key=W,Scale=2.000000)
AxisMappings=(AxisName="MoveRight",Key=A,Scale=-2.000000)
AxisMappings=(AxisName="MoveRight",Key=D,Scale=2 .000000)
AxisMappings=(AxisName="MoveRight",Key=Gamepad_LeftX,Scale=1.000000)
AxisMappings=(AxisName="MoveUp",Key=E,Scale=1.000000)
AxisMappings=(AxisName="MoveUp",Key=Q,Scale=-1.000000)
AxisMappings=(AxisName="Turn",Key=Gamepad_RightX,Scale=1.000000)
AxisMappings=(AxisName="Turn",Key=MouseX,Scale=1.000000)
AxisMappings=(AxisName="Turn",Key=Seven,Scale=1.000000)
AxisMappings=(AxisName="Turn",Key=Six,Scale=-1.000000)
AxisMappings=(AxisName="OculusRemoteMoveForward",Key=OculusRemote_DPad_Up,Scale=1.000000)
AxisMappings=(AxisName="MoveForward",Key=OculusRemote_DPad_Down,Scale=-1.000000)
AxisMappings=(AxisName="MoveForward",Key=Up,Scale=1.000000)
AxisMappings=(AxisName="MoveForward",Key=Down,Scale=-1.000000)
AxisMappings=(AxisName="OculusRemoteTurnAxis",Key=OculusRemote_DPad_Left,Scale=-1.000000)
AxisMappings=(AxisName="OculusRemoteTurnAxis",Key=OculusRemote_DPad_Right,Scale=1.000000)
AxisMappings=(AxisName="Turn",Key=Left,Scale=-0.500000)
AxisMappings=(AxisName="Turn",Key=Right,Scale=0.500000)

Wherever it says 2.000000, replace that with whatever you want the movement speed multiplier to be. 2.000000 is what I feel like the basegame movement speed should have been, though going higher might suit your preference better.