Most everything has already been said, by sources with WAY more experience than myself, but since your Fury is the same age as my New Yorker (see photo) metallic with original finish, and I started with little knowledge, maybe my $.02 will help.....
I found the following link helpful:
The Secret to Removing Oxidation and Restoring a Show Car Finish to Antique Single Stage Paints
I started with this, with some advice from others on here, and had reasonably good results. Out of an abundance of caution (and lack of knowledge) I did the least "aggressive" sounding steps skipping the clay bar as I was afraid of doing damage with it. No buffer got anywhere near the car. Here's what I noticed:
The Meguiar's #7 was gentle, and really seemed to lubricate the finish. I did the whole car with about half a bottle. Takes a while to remove, but seemed to make the paint easier to work on too.
I stuck with the most natural products, avoiding abrasives or chemicals. After the Meguiar's, I used Zymol cleaner/wax, which was a liquid. Finally I used a couple coats of carnuba wax, using only a sponge applicator, and soft cotton cloths. Step by step the finish brightened up a good bit. Definitely not as well as the red Polara, but I got a good sheen, and the cloudiness went away. A goodnumber of spots, blotches, etc., remain, but the paint is preserved, and presentable. Didn't know about the Dawn wash, sounds like a good first step. Good luck, and hope this helps.