The proper way to clean is with water and aluminum foil. Wet the pan over heat, and gently scrub away and cooking residue with a handful/clump of aluminum foil - empty, rinse, repeat until clean. Next, blot any remaining water and wipe the pan down with a light coat of oil. It is now ready to store.
Soap can breakdown and remove the seasoned coating. Aluminum foil is used because it is softer than the seasoned coating, but will remove food particles.
This comes from decades of camp cooking on cast iron - skillets, frying pans, Dutch ovens - both on stoves and open fires. Aside from the weight, there is no better outdoor cookware (and indoor if you have a gas stove).
You have to stay on top of it. If you soak it and forget it it will eventually get covered by the black crud, which is water soluble so it's not as tough as rust to remove, it can be brushed off, still a pain in the ass.
Better monitoring the progress and take the part off the bath once rust free, then rinse in water and then apply a rust preventive solution (i.e. rust bandit). I did a bunch of parts that were then yellow zinc coated...turned out better than new.
I've also tried the technique of 'rinsing' the part with rust remover using a fish tank pump to spray it, it worked rather well and prevented the crud from forming as the solution is always moving on the surface being cleaned.
I've used Metal Rescue and it worked the best but it was too expensive and at the time could not be purchased concentrated, then I've used Esprit Rust Remover, still have a gallon of concentrated. The gel worked to even though I found it less efficient.