If zinc is more reactive than silver, store your silver in zinc plated boxes and instead of the silver tarnishing in contact with sulfur in the air, the zinc will oxidise. So long as the silver is in electrical contact with the metal of the container with the galvanised plating it will stop corrosion. eg a stack of bare coins sitting on the galvanised surface would all be protected.
Zinc will work and so will copper. Just get a bar of zinc or copper and put it in the same container as the silver. The silver tarnish is Sulphur rather than oxygen. I have a couple of copper rounds mixed in with my silver and it seems to work pretty well.
