Taking inspiration from SR785 on how it reads differential signal, I figured that acromag too always need a way to return current through RTN ports always. That must be the reason why everything goes haywire when RTN is not connected to IN-. Now for single ended signals, we can always short RTN to IN- and keep same GND but then we need to be careful in avoiding ground loops. I'm gonna post a wiring diagram in next post to show how if two signal sources connect to each other separately, a GND loop can be formed if we tie each IN- port to RTN on an acromag.
Coming to the issue of reading a differential signal, what SR785 does is that it connects 50 Ohm resistance between Earth GND and differential signal shields (which are supposed to signal GND). In a floating GND setting, SR785 connects a 1 MOhm resistor between input shield and Earth GND. This can be used to read a differential signal through a single BNC cable since the shiled can take arbitrary voltages thanks ti the 1 MOhm resistor.

We can do the same in acromag. Instead of shorting RTN to IN- ports, we can connect them through a large resistor which would let IN- float but will give a path for current to return through RTN ports. Attached here are few scenarios where I connected IN- to RTN throguh wire, 820 Ohms, 10kOhms and 1MOhms in two sub cases where RTN was left open or was shorted to Earth GND. In all cases, the signal was produced by a 9V battery outputing roughly 8.16V. It seems that 10kOhm resistor between RTN and IN- with RTN connected to Earth GND is the best scenario noise wise. I'll post more results and a wiring diagram soon.