do your monitors have balanced inputs?
Balanced and Unbalanced isn't so much a shielding/ grounding issue as a level / voltage issue.
Balanced = "pro" level of +4 DBv
Unbalanced = "consumer" level of -10 DBv
or about 1 VDC of signal difference to a 600 ohm load, if memory serves.
In other words you'll need to adjust gain a bit to compensate.
FWIW, Eveanna Manley stated strong doubts on the benefits of balanced interconnects.
(She's my kinda gal)