True, upside down is bad. For most big-box store installs mounting an amp to a box is safe (assuming 300-500W low end subs). Getting into high power/high performance, a lot of amps fail from vibration damage, also makes it much easier for thieves to grab the whole thing and go real quick.
That amp is a monster, does easily rated 4K at real world voltage and impedence and they have been clamped at around 10KW on 18V. Broke one of my subs day 1 testing, which is cool since I want to build them up with some different coils and go up to 18".... I wasn't really going easy on them.
I actually haven't checked what's under the carpet in the back. I had considered using some liquid nails and mounting a piece of ply right to whatever it is that I could screw things down into, but I can't afford the space and whatever I put in should be snug enough to not move around much. If you investigate under the carpet LMK what you find. My big fear with drilling into that area of any car is going into the gas tank or something else dangerous or important.