Have you tried to figure out a way to actually mount it to the bottom of the seat?
It seems like it's just plastic under there. Strong plastic, but I don't think self tapping screws would do that trick. Not too sure though.
Alright. I've finally got my install complete. I decided to put my pc under the passenger seat and the screen in the dash. I didn't do any modifications to the car itself, except for the 4 screws holding the pc to the floor.