I have tried 3 sets...

When does the shutdown occur, under system/gaming load? Surfing the net?

Did you ever formally rule out the PSU itself and the memory?

Completely random: gaming, browsing Windows, BIOS (once), media player. Shop tested different RAM, I ran HCI Memtest extensively, I ran the OCCT PSU stress test but don't have another (unsure if the shop tried one - shut down only happened once to them in the 1.5 weeks they test the system.

Doubtful the shop tested another PSU. And how extensively did they test other RAM?

I still don't like this Corsair memory set on the Z170 platform.
Can't you get a 3000MHz TridentZ set from Newegg to test for 30 days and return if it doesn't work out?

They did say they also measured the PSU outputs and stuff, but I also doubt they extensively tested my unit. You think RAM can cause this strangely random issue? Ordering at Newegg costs me insane tax and shipping costs. I can get a kit from here with no possibility of returning it for a refund (http://www.gskill.com/en/product/f4-3000c15d-16gtz - it's a two stick kit though) - why don't you particularly like my memory kit?

I am leaning towards a PSU RMA, since the cable reseating is the only thing that gets it booting afterwards.

RMA the PSU and stick with the stick cables for now.

Any type of connection is the weak link in a circuit, that is the drawback of modular cables, I don't know if it is your problem or the cause of your unknown error code, but modular cables do have the potential for a connection failure even if not a full open, a high resistance from poor, uneven contact that can get worse over time from humidity, vibration, etc. I have not experienced it with the Corsair cables myself, at least not that I know of, I have experienced a lot of problems with different 4 pin molex connectors of poor quality, when modular cables first started being used many people would not use them because of the potential of a high resistance connection, every time you insert, remove a cable has the potential to weaken the connection ever so slightly, if every single wire were separate, with a separate connection it would be rather easy to determine but with say the 24 pin cable there is no way to determine that 1 of the 24 has a weak connection
I had purchased the very first power supply that EVGA released and had mysterious failures issues while benchmarking, under high current draw, EVGA determined the issue was a single wire on a 3 volt rail was of to small gauge and sent me a new 24 pin cable
Again not saying this is the cause of your issue