Thanks for the reply! I'll try and figure out what to do.thanks for the pic, glad you like them!
The only problem you might run into is drawers clearing the tailgate. On most (mine included) the bottom tailgate does not open flat, but at a slight angle - this is why the drawers are spaced up and you see that bottom front spacer in your directions. If you install over sheet metal I would simply shim the front whatever depth needed to make up the missing carpet and sound deadener - plywood is fine, buy the small 2x4' "work" panels at home depot et al - it won't be visible so could be any grade. Also, I'm not positive the 3rd row seat brackets which 100 series bolt into might need some washers to shim up as well, I don't remember if those brackets were metal-on-metal with the frame or resting on the carpet... either way the answer would be yes you can, just need a few shims, no mods to the drawers.
As for noise, it's a good point by @ScubaJon but I suspect the layers of plywood and loaded drawers will act as deadeners on their own. You can always install without that, drive and try it (and please report findings!) and then take them out & install deadener later if needed.