Yes, it must be insulated from the chassis.
The shielded jack you posted must have been wired wrong or defective. It should have acted the same as the other did when it was grounded to chassis.
Also, the noise you experienced must be due to the dress of the wires. Where you routed it through the back of the chassis must be a sensitive area.
An insulated jack mounted where the original speaker wire went through the chassis should not pick up any more noise than the original wires did in the same spot.
The shielded jack you posted must have been wired wrong or defective. It should have acted the same as the other did when it was grounded to chassis.
Also, the noise you experienced must be due to the dress of the wires. Where you routed it through the back of the chassis must be a sensitive area.
An insulated jack mounted where the original speaker wire went through the chassis should not pick up any more noise than the original wires did in the same spot.