If your furniture is truely cast iron, and no-one else objects, then I can't see any reason why you couldn't have them sand blasted. I had a customer who remove his cast iron railings and sent them out to be blasted. When they came back, there was some minor pitting but other than that they were in great shape. I primed them with XIM primer an finished with Brunning's Silithane.
The only other thing I could think of is to take them to someone who does "dipping" with a methylene chloride stripper. Most other strippers are "wet" and will lead to "flash rust".
Wait and see if someone else here has any input. You may get some better suggestions.