Very carefully! Here's the worst of the damage:
http://i890.photobucket.com/albums/a...id_damage3.jpg
Fortunately, there are enough areas around the transistor package that was eaten (now removed) to make some connections, so it is repairable, but the area in the photo is extremely small so I will need to glue down the eaten traces that are usable and then make up a jigsaw piece with a new XN4608 and thin wire to remake those connections.
Incidentally, if anyone has that package that they would be willing to donate to Barney's cause, please PM me - it will be a few weeks before I am ordering any SMD parts and I don't have that or a usable replacement in stock. After seeing the damage to this radio I've taken this on as a "let's see what we can do" project so I'm not charging anything for what I'm doing.
As for preventing further deterioration, I'm gently scraping off the damaged areas and using a soft brush and alcohol, then repairing as necessary.
This is the last of the major damage though so hopefully after sorting this out, we'll have a working radio.