Dugan, I use B-I-N often and love it but I would go with Sherwin-Willians recommendation on this.
B-I-N is a shellac product which is great for drywall or plaster walls but I would not use it on metal. Since alcohol is the solvent, you can get pretty lightheaded using it in a closed area when the alcohol evaporates. Since I like B-I-N so much, I don't have experience with Bullseye 1-2-3 but I am not wild about using a water based product on metal even if Zinsser's product brochure says it should be an excellent choice.
If you stick with Sherwin-Williams products and recommendations, you know who to go to if you have a problem. Your local store has an interest is seeing that you get good results since they want you back for future needs and they hope your reports will be good word-of-mouth advertising for them.
If your paint is in good condition, you should have no worries about rust on the painted side. You concern will be rust from the back and a rust inhibitor will do nothing about that. Unless you want to pull down all the ceiling and back prime all the metal before reinstalling it, there is not much else that you can do and a rust inhibitor will not help otherwise.