Measured voltages on 2 cards that function fine on High.
Card 1
C099-103 | Low 1.063V | High 1.186V
C083-087 | Low 1.062V | High 1.186V
Card 1
C099-103 | Low 1.057V | C099-103 High 1.178V
C083-087 | Low 1.062V | C083-087 High 1.185V
The 'problem' card's voltages are comparable to these so at least that part of the voltage delivery is fine.
Removed and re-soldered the 14.318 MHz oscillator just for kicks.
In retrospect that doesn't make any sense since one oscillator is for both banks.

Good practice though. The smell of flux. The shine of solder. Good times.
Concerned it really was just a power issue I put the Cube back on the Seasonic 860w PSU and High clock behaves as expected for the chips that are not all x'd up, but the issue with the dead bank is still present.
The 700w OCZ700GXSSLI, which technically should have enough oomph, is old and apparently does not quite chop the ketchup... no matter how hard I wish it.
The chips on the mystery bank have come back alive a couple times but it does not seem to be consistently reproducible.
Sometimes a reboot will do it. Other times powering off and powering on the PSU. Most of the time none of that works, times such as right now.
I am tempted to Fonzi the cube but if that worked I'd have to get back into voodoo.