I hate to make this thread any more complicated... but here goes. Multiple ground rods don't cause a problem when they're all bonded together. That problem arises when you have an isolated ground (power comes from the service panel but goes to a separate ground that isn't tied back to the panel).
In the case of our welders, we're adding a shorter path to ground that is bonded to our service panel ground through the welder's chassis and will not cause a problem.