Man you guys mounts cost more than my TV.....is this a Mercedes or something. Good luck with the door. While it seems solid, pretty sure it is paper thin. I was trying to use a screw one time while attempting to attach/secure my stow away lower bed platform and the screw went right on in. There definitely has to be some studs there but no idea where. Running the cable sounds like another project but that appears to be how we or at least I spend 1/2 my time - updating not camping.
Oh well, whatever you do - post it up. There are likely a few folks with the same idea and will want to know how it all goes. Good luck.