Welcome to the forum. I plumbed my iron filter and softer into both hot and cold. I plumbed one outside hose bib before the iron filter and three more of them after the iron filter but before the softener. Two more hose bibs provide hot and cold soft water.
I agree that the busted bladder exposed the iron to air and the water to the steel of the tank. Unless you are getting sand into your bladder tank, I would not worry about trapping anything before the tank. If you are getting sand, a Lakos sand trap would be in order.
We didn't like the taste of our water either and so installed a R/O filter with a spigot at the kitchen sink. I don't buy the argument about R/O water being bad for you, stripping out minerals. We get all the minerals we need from the food we eat. Soft water is not unnatural, hard water is. Before man evolved to drill wells and pull hard water out of the ground, we drank mostly rain water which is soft.