CrossRoads:
Think about how you use a multimeter - you just have 2 leads, the meter is 'floating' and only connected to what is being measured.
Use the relays the same way.
Connect all the Commons from one side of the shunts to arduino GND.
Connect all the Commons from the other side of the shunts to an arduino analog input.
The Normally Open side of relays connects to the shunts.
The Normally Closed side is not connected.
When you want to make a measurement, drive the coil for 1 and only 1 relay. The arduino GND and Analog inputs are now connected to the 2 sides of the shunt and you can take a reading.
The Arduino GND is not connected to the rest of the circuit so it can act like a floating multimeter.
Interesting idea. May I ask why dpdt?