Good work! That was totally worth the effort to fix, those are neat machines.
FWIW I might have tried an electrolysis tank to remove the rust. Basically what it involves is a solution of water and washing soda and a DC power supply. You hook up one end of the power supply (negative) to the item that needs to be de-rusted, and the other (positive) to a consumable iron rod that is facing, but not touching, the rust spot. Both are submerged in the liquid solution. When power is turned on, the rust is slowly removed by a chemical reaction.
Hooking the power supply up the other way actually creates rust on the object in question - also kind of a cool trick if you want something to look old.
I've done this to a couple of antique rifles and some old tools that were in bad shape. The results are amazing. It does produce hydrogen gas and some fumes so it should be done outdoors.