That box looks perfect go off that. As far as clipping it's when the voltage produced by the electrical is too low for the voltage produced by the amplifier and causes the amplifier to clip sine waves to compensate, which will cause kick offs, bottom outs and worst of all a blown coil. The BRZ does rated but ONLY at 14.4v so if you're only getting 12.7v thats FAR from enough you're probably getting more like 1500RMS. Also it doesnt matter how high your volume is or how high it goes some headunits go up to 63 like mine but you want to play around 3/4 volume.
It also helps to know what headunit you have to figure out the preouts, if you have 4v that amplifier is turned way too high if you have 2v then it could be something else. I think it's a lot of LITTLE things causing your problem. Your electrical isn't too bad but from the drop youve described thats really low.
Start off with a new box, turn your gains down and learn how to setup gains with a multimeter.