I'm likely not the one to give advice. I not only don't know anything, heck, I don't even suspect anything.
But I do have a diamond-plate cross-bed tool box in my '90 F150 extended cab pickup. Came with the truck, and it's handy. The truck's only jacked up a couple of inches. The toolbox is about 16 inches deep, and I can reach over the sides to get at stuff down to the bottom about two feet in, from both sides -- I bolted down a couple of chunks of 2x4 to keep things I might need quick in an emergency (jack, flares, 1st aid kit) from sliding to the middle, so it's always in reach.
I keep the back seat down, don't have extra passengers -- my old lab rides in a dog-bed back there, leaves half the back seat for the stuff I do need to get at fast, rain or shine -- tool box, coats, etc. I don't know about anyone else, but I don't mind climbing into the bed to get things I don't use often, like jumper cables, shovel, ax, kitty litter for traction. Even at 77, climbing up is no big deal.
Only thing I don't like about the tool-box is, I have to remove it to get my little 4x4 UTV into the bed. I know, I could use a trailer, but why?