Just thinking, the first stage is the highest gain and the most vulnerable. (Of course vulnerability is a function of length of the connection and whether or not it is in the bundle.)
But, I was thinking the very first input from the jack could be shielded by the wire wrap method. Perhaps a single or twisted 2 or 3 telephone company wires wrapped on the bare wires.
Also, would it be equivalent to say shield the signal path in place of the grids?