If you do lift up the carpet (I recommend it!) you could put a piece of thin ply or MDF with scre holes to attach to the amp, not the car floor. using some tapered headed metal threads to secure the board throught the carpet to the amp, using a few neatly cut holes, would secure the amp quite well. A little bit of work but quite a safe option. Put some small rubber or felt feet on the back of the screw heads to stop them searing a hole in the paintwork and it's all good.