The main issue we are having is the floating ground on the BNC ports of the zotino channels.
Just to avoid confusion, the Zotino BNC outputs are not floating at DC. What you are seeing is more likely a "good old" ground loop between amplifier output, your earth reference ground, and the Kasli mains supply ground.
As sb10q points out, you might be able to avoid this, i.e., turn Zotino into a floating voltage supply, by using a Class II supply and making sure you don't have any other unintended ground connections. (Running Zotino from a separate DRTIO satellite can be handy to resolve ground loops between different parts of your system.)