Hi! Do I have to apologize for necromancy if I'm OP? Not sure.
After a great many shenanigans involving the CPU cooling, the CPU itself, and the BIOS chip, I've finally been able to both boot unRAID and close the case. Now only the first row of hot swap bays is registering.
So I bought the following cables:
2 of these: http://a.co/7LX74v9
1 of these: http://a.co/4wqwEpT
The bottom row (the working one) is using the 4-to-1 cable, the other two rows (the non-working ones), are using the 1-to-1 cables. I suspect this is not a coincidence, but can't tell where I went wrong.