What about the handles and levers. Can they go in the solution too? ( with crud cutter?…)If you neglect a steel or iron tool, it's going to rust, even in a garage or shop.
This clamp looks like it has mostly surface rust. There might be some slight pitting or discoloration when cleaned up.
I might give it a bath in a rust remover product then clean it up with fine steel wool. Maybe somebody else has a better suggestion.
I love this guy's videos: