NOt clear where you are connecting the shutdown controller; make sure you follow the instructions
THe main voltage connection should be
Battery -> Shutdown controller -> Inverter -> Regular computer PSU
do not put the inverter before the shutdown controller!
no need for a cap, you're not driving a Subwoofer (somebody back me up on this, the only reason for a cap might be to survive cranking, but I don't think that the cap would hold enough charge for this)