I just wanted to throw this tip out there for anyone with an oxidized compass and a limited budget.
My boat came with an Italian-made compass, a Riviera Urania. The compass globe was so badly oxidized that you couldn't read the dial. After finding out that there is no one in the US that services these compasses, I looked into buying a new one, but did not have three or four Benjamins burning a hole in my pocket.
I was watching TV one night and saw an ad for a headlight lens restoring product and I thought that that type of thing might work on a compass globe. They are both plastics with the same problem, right?
I didn't buy the As Seen on TV product, but picked up a Turtle Wax Lens Restoring kit instead. Amazon.com: Turtle Wax T-240KT Headlight Lens Restorer Kit: Automotive
It is basically a four or five step sanding process followed by a polishing and sealing step. About an hours worth of elbow grease later I was pretty impressed. There is still some deep crazing that will never come out, but what was an unusable instrument is now usable. See the before and after pictures below.
*Full disclosure: I have no financial interest or connection with Turtle Wax.