I would bet that rust on the "service" scroll will clean off with barkeeper's friend, but as other have said, don't scrub too hard or it will dull the shine. The rust on the grommets probably won't clean up much since it's usually deeper there. That's on the edge of the field anyway so if it were me, I'd just try and clean up that first spot and then leave it. That's your choice though. Gorgeous sign BTW.

Brian H