If thats the case, im not so sure id want to risk 1 header running 6 fans, whilst waiting for your case to be replaced, grab one of these, the supplied cable goes to the motherboard header for PWM signal only, then it requires an SATA power connector to supply power to all of the fans, great option for the price, well worth it:
https://www.overclockers.co.uk/xspc-8-way-pwm-splitter-hub-sata-powered-black-v2-fg-009-xs.html
There is however another option, if you have any old devices laying around with a molex connector on them, you can cut the molex off and use that, in your picture where is says "input", remove the VCC and GND wires from the supplied cable (motherboard end) and connect the molex connector, now your fans are getting their power from the molex connector and the PWM signal is being supplied by the motherboard.