I would avoid the WTSHTF commentary because it is a frowned upon subject in this forum, plus you will face public humiliation and rude treatment rather than a simple or polite "hey can you change that" note. So I will carry on "hypothetically" discussing inverter usage in a survival scenario
I like that you treat your rig like a prized possession, mine used to spend its life in a storage facility too! I'm almost to the point of buying another one just to beat on because this M1031 is in such great shape.
That inverter is a big boy, I think the only place you could mount it with enough clearance would be on the back of the cab as far down as possible behind the seat. The good news is that the unit does have remote panel capability so you could mount it anywhere and still be able to switch it on or off. Not sure if it comes with that panel or you need to buy one. I do know my Xantrex has one that connects using an old style phone cable (RJ11 or 45?) and it gives you a ton of info like battery voltages, current draw, etc.
Now having said that, for the near $700 that will cost you...would it be better just to buy a Honda EU2000i or similarly sized Yamaha equivalent? You can even get a slightly lower quality inverter genset for $500-700. Much more portable and you don't have to keep your truck running. The little guy would consume .5 to .75 gallons of gas for 8 hours run time, the 6.2 diesel is a lot more and much noisier. Just throwing it out there. Then you could just get a little inverter for charging phones and computers in the truck while on the go. Not to derail the thread, just throwing out discussion topics.