You got some experts to help you out but one thing i know about s4 and rockmars amp is its a worse combination..
No need to buy a d4. Just buy a mono or a decent 2channel amp that gives out around 350 or 400 watts rms. Rockmars amps claim to give out 200watts rms when bridged but i doubt it. Even if its true, 200watts are not enough for your sub. What the shopkeepers do is increase the gain to make it louder on low volume but when you turn up the volume, sub starts clipping resulting in damaging the coil and muddy and noisy bass.
Source= i own a s4 and rockmars amp i used my friend's Pioneer gm-5100T for few days and i could really feel the air passing down the seats and kinda feeling that hairs are moving.. Backview mirror was turned arund with the first hit..
About the STP sheets, i read on a forum that using the thin foam alongwith foil paper does the job as well. Not as good as the proper sheets but about 60-70% improvement. That thin foam is available on all carpet shops. Usually of red or blue color.
About the new box.. what kind of bass you want? One that hits the lows well or just louder? I know you want both but which one is preferred?