You are always going to see something from neutral to ground considering that the neutral is current carrying and the ground is not. Any voltage drop on the neutral is going to be reflected as a difference to ground. This gets even more pronounced with sub panel feeders and heavy line to neutral loads. I wouldn't doubt that when the heating element in a laser printer (or copier) cycles it causes a 6 volt spike. I also doubt that it is having an effect on the copier. Matter of fact I wonder if it is the copier itself that is causing the spike.
What I would do is run a dedicated back to the service panel. Don't take it from a sub if there are any.
-Hal