056080 is just ordinary Maytag transmission oil and it's still readily available from any number of sources, including eBay. I've recently seen it listed as 6-0560800 at repair clinic as well. Some folks hate this stuff and complain that it reeks of sulfur, but sulfur is a lubricant, so there you go.

As for resurfacing the damper, if the surface that contacts the damper pads is corroded, gouged up or otherwise marred, I'd replace it with a new one. Unless the defects are really minor, it'd be very difficult to remove them without altering the contour. The part number for the damper is 203725, and it's another one of those parts that are still found all over the place, including many online vendors. On the other hand, if you're talking about the area on the base plate where the damper pads are glued in place, that's a different story. I'd imagine the corrosion there would have to be very severe before the pitting left behind by its removal would cause a problem, and that pitting could be filled in with Bondo prior to painting the base plate and installing the damper pads.