SajinEvga support can assist with cable replacements. You sure the cables are fully secure?
sparetimepcSo did you reroute the cables so the back panel doesn't even touch the cables, like don't even route them around the back side temporarily to make sure the back panel itself isn't grounding out something or the motherboard plug itself isn't defective? I believe that's a modular power supply, did you try a different cable. This seems like your not leaving enough room for cable movement. Make sure there is no solder point sticking out on back that when putting on the back panel it's pushing a cable hard enough to penetrate it.
EVGATech_LeeMSimilar to what sparetimepc suggested, are the cables stretched or overly tightened at any point for cable management reasons? I'd concentrate by looking at the ends of the 24pin connector - on both sides - to see if a pin is backing/pulling out of the molex connector. That could easily be the reason why it's shutting off.
HoggleI would be taking it apart and finding out if I can spot the damage on any cable. Power cable issues can go very bad very quickly. I would also be looking for any part where a cable could have been near a case fan or the edge of something you might have moved like the side panel that could have caused damage.