Those figures are WAY off what they should be,
but I strongly suspect they're wrong. Many people have the same issue of voltages incorrectly reported and they seem to be somewhat similar to the ones you list, so it looks like the only way to see the actual values would be with a multimeter. The system wouldn't boot with 8v on the 12v lines.
And I was wrong about the 500W requirement, sorry, seems that 500W is the
recommended minimum for your combination of CPU / GPU, so 650W still has some headroom. All the newer PSU's are switching to improve efficiency and include filtering and smoothing, so by the time the power is coming out the PSU it's been quite well conditioned. Quite often a faulty capacitor can cause problems, though. I have a Zalman 600W PSU that made one particular motherboard of mine really struggle to boot. Replaced a couple of capacitors with higher quality ones and hey presto, better than new
So I'm afraid we're not much closer to a solution yet, but I do think it has at least a little to do with regulation / smoothing / ripple / noise / interference on one of the lines.