Hi, Beth. A paint stripper is the way to start cleaning up to tin ceiling pieces, but don't use a putty knife for the stripper/paint goo removal. You can get stripping pads marketed by 3M and Citristrip at home centers. An old plastic bottle, like for laundry detergent, with the top cup off makes for a good place to scrape the goo off. Be gentle with the stripping and let the stripper do the work. Be sure to wear rubber gloves (not latex) and eye protection. Wash the tiles off with paint thinner/mineral spirits after stripping. Naval jelly should get any rust off.
If the tiles are going to be around before installation, you might want to put on a light coat of clear lacquer on them, front and rear, to prevent any rusting.
I'm not sure what you want to do with patina. The ceiling tiles were always painted in the old days to prevent rust and to match the other ceilings. You can get chemicals that will give you a pretty good representation of patina but not quite the same as the surface that aging 100 years would give you. But then we are back to why you want the patina. If you do go this way, I would spray on flat lacquer for protection.