I always use the chassis. You can get shoulder washers and insulating washers that will completely insulate the conductor(s) from the chassis. McMaster-Carr, Digi-Key, Mouser, etc. should all have a decent selection
Be aware that coupling of grounds is likely to degrade crosstalk between channels and/or bleed-through between inputs, relative to the existing performance. Ground is not equipotential if current is flowing through it, including the return currents of inputs and outputs.Regarding grounding: There are both input and output jacks on this panel, which have different ground points. Also, each output jack gets it's own ground. I'm not sure if I can share these or not, for now I'm trying to copy the original schematic.