My recommendation is to ground the tone arm and turntable to the Piccolo separately. Sometimes you have to ground the table, other times you do not. Sometimes you get a hum grounding the table but get static discharges if you do not ground the arm. This gives you maximum flexibility.
Ground the Piccolo to the CornetII only if you hear a hum. As you mentioned, the remainder of the equipment will ground through the RCAs.
BTW, when you can, please send me the order numbers for the screw down green connectors you use for resistance loading. I want to run these on a CineMag SUT I am building now. These are just way too juicy.