With regard to your two points:
1. For your circuit, I would definitely place the board in a shielded enclosure. The enclosure should be "grounded" to your circuit power supply common. What you want to do is provide a return path for induced current, but you want it to be somewhere else but your sensitive trace. The way to do that is to surround the circuit with a well grounded cage.
2. For your nearby "high" voltage pins, you could simply place a short "ground" trace stub between the sensitive pin and the "high" voltage pin. That would give leakage current a return path other than your sensitive pin. The trace can be thin and should be short - its only job is to provide a drain for leakage current to keep it away from your protected pin.
I used quotes around the term "ground" above because it is a general term for whatever the common voltage reference is for your circuit board.
In both cases, the goal is to provide stray fields and current with a lower impedance (hence easier) path than your sensitive trace or pins. The current will flow somewhere, it's your job to make it flow where you want.