What are some easily-undertaken reactions that will precipitate or restore the iron from rust, in a non-lab context?
If you have a plastic bowl or container large enough to accommodate your item, fill it with water with with some salt (e.g., kitchen salt).  Then you need Aluminum foil lightly wrapping your rusty piece of iron which altogether are immersed in this said solution (luke warm is enough).  One important detail is that the foil is in mechanical contact to the iron, while the solution is able to be in contact with the foil and the cast iron simultaneously.

Over the course of the next hours, Aluminum will be "eaten away" -- or, more chemically speaking, Aluminum will be oxidized, and the rusty iron will be reduced.  To facilitate the process, it does not harm to scratch the Aluminum surface with a brusch on the surface exposed toward your iron pieces.

To direct the work of this oxy-reduction reaction toward your rusty iron pieces, it is important that the container for this setup itself is not made of metal.  Depending on the size of the item "to recover" things like a glass / china bowl, or a plastic bucket are suitable.  After half a day or so, remove your item, rinse it with water and a brush; dry it and protect it against new corrosion.  As already mentioned by you, this may be done by galvanizing, or by galvanic anodes.

An alternative to using a salt solution is the addition of vinegar to the water.  The key point of both (salt or vinegar) is that they increase the electric conductivity of the solution, hence accelerating the process.  If using vinegar, however, do not forget to protect your hands with gloves and eyes (goggle) against the acid.