If you get the set going, and don't mind making a trip to Omaha NE with the cabinet. I know of a man and wife team that does suburb work on old furniture and cabinets. Titan1a recently had a 1936 Philco radio cabinet redone and they did a super job. The radio was moisture and/or weather beaten, and after they were done it looked just like brand new. I suggest that whom ever does the job that you remove the entire electronic "guts" as sanding, staining, and finishing could really mess up the unit itself. It would be quite a trip for you (twice), but they do very good work. Here is a link with reviews of the place. If you by any chance you do make a a trip to Omaha, I would be willing to tackle the record changer.
https://www.yelp.com/biz/wooden-ways...den-days-omaha