Dude asked about where to put a spare tire, not how in the world is he ever going to put a camper on THAT truck! Btw nice clean looking pickup in your sig..! 90s models GMs are some of the best out there!
Oh, and the 300lb thing.....not correct. You'll lose the dead weight of the spare, maybe plus a tad for it being a bit behind the rear axle.
Assuming 80lb tire/rim, mounted 3' fwd of front axle, 12' c to c on the axles the spare tire will take 20lbs off the rear axle. That's the resultant force required at the rear axle location to off set the tire weight that is now cantilvering off the front axle.
Static moment diagram.