Mick,
I too suspect the wall wart. I'll assume that it's a DC output with a voltage of somewhere between 12 and 24 volts? In any case, I think the bridge rectifier in the wall wart has an issue or two and is letting in some pulsating DC, or even some AC into the circuit. I suspect the wall wart may not be "technically defective", but is on the boarder of being out of electrical specifications.
I'm not that familiar with that table or the wall wart, but can I ask if the wall wart has polarized plugs, and if not, have you tried turning the wall wart 180° so the other plug side goes to the hot. If the plug is polarized, then there is nothing you can do except, replace it.
To summarize, I do suspect some AC component getting passed, and no grounding scheme or technique will fix this problem. Perhaps a better power supply (not a wall wart) may be the answer.
Wayner