Summing Mixer Amp - Balanced or Unbalanced?

[abbey road d enfer]

This looks like a potential giant ground loop to me. I would use shielded 2-conductor cable off of each jack, then tie all grounds "starred" at one point.

Nonsense. With balanced connections, the shield carries no signal. They all come from a single point, the converter. Connecting them to a star point or bussing them makes no difference.
Actually, they may well be left floating on one side.