I found an old bottle of Birchwood-Casey (B-C) Blue & Rust Remover in some of Dad's stuff, and put it to good use. Using it with steel wool made quick work of removing the old rust and finish, especially the brown coating of Blue Wonder from six years previous, which came off easily.
I did the blue removal at a sink, but it wasn't my wife's kitchen sink! The B-C Blue Remover has a strong odor and it's pretty aggressive, and I wasn't about to risk life and limb by polluting the air and surfaces in our house. Instead, I worked in an outbuilding that has its own sink.
After treatment with the remover using steel wool (just follow the instructions on the bottle), I rinsed each part with cold water under the faucet, making sure to get all of the remover off. In some cases I washed the parts with cold water and dish soap to make sure I got all the nooks and crannies clean. When I was satisfied that all the old finish, rust, and remover were gone, I dried the parts and took this photo.
After that it was time to de-grease them and hang them up so I could shoot them with B-C's new Perma Fin, using an airbrush.