Wow, that is one strange looking truck.
New to this forum so I don't know if the following has been posted, so I will just post it anyways. I have built over 2 dozen food carts/trucks over the past few years so my method for making things look like a 50s toaster is well tested on various applications. I have mirror finished a 57 Silver Streak trailer, a couple canned ham trailers, and a few trucks, same process every time.
Most Home Depots carry a stripper by Jasco, multi purpose. The stuff is fairly evil (I got burn marks to prove that), and removes most anything, including the hair on your arms.
Jasco and a straight razor blade, let it sit a minute or two until it is bubbly, scrape it off. While this method has a higher chance of burnt flesh it is far less messy then power washing it off (tried it the first time, stripper soaked paint chips all over). First go over will remove 80% or more. Go over it a second time, you can use a green brillo scrub pad to loosen the tough spots. Rinse and repeat.
Once you have bare metal soak a rag or three in mineral spirits or lacquer thinner and wax on wax off. This will remove the residue.
Final and slowest and most annoying part. 3M makes a line of rubbing compounds. Heavy duty rubbing compound is the one you want. It isn't usually sold on shelves but Napa carries it at the warehouse, costs like 60 dollars for a gallon. Go to harbor freight and buy a variable speed buffer, get some wool pads while your there. Apply a gob to said wool pad, start at very low RPM and work it into a area about 4'x4', slowly increase the RPM. Compound will turn black, that means your on the right track. Keep buffing and before long you will see your ugly mug smiling back.
Tedious yea, but you can turn near anything mirror gloss this way. Aluminum works best, but I have done it to steel as well.
About to do it on my own truck, if I make it to 30 posts and 30 days I will post pictures.