I cleaned a cast iron bath tub with a toilet bowl cleaner
The bowl cleaner temporarily removed the tubs resurfacing rust; an increasingly browning film stain. But probably too well; also dissolving away some of the tub's enamel. You'll want to find a balance between removing just enough brown film stain routinely; while not dissolving too much enamel. I suggest a lesser strength acidic cleaner, and rinse it off sooner, and very thoroughly. Unlike your tub, toilet bowls don't have an under laying iron frame, so rust can't resurface... Good luck, take it easy, and think about a replacement tub sometime. Long term, I that's a better deal, than "painting it". I'd like to buy stainless tubs, sinks, and toilets.