Oscilloscope measurement: unsure how to connect the scope ground to the target
You still need to connect the junction of the joined probe earths to something on the target system. Why not use a multimeter and check that earth on the scope (AC plug) corresponds with 0V on the target system. If there is a significant fluctuation in that measurement (AC) it may be because the target system is floating i.e. does not form an earth connection at all.

If the latter is the case then try connecting its negative pole to earth potential through a resistor at first (maybe 100 kohm). Check to see the voltage across the resistor using just the probe end on the scope. Consider gradually lowering the resistor and see what happens to the scope voltage - does it reduce - if so then it's likely the target is floating from earth and can be directly connected to earth.