I'd've
My personal take on this is that if a word exists in oral use, it can always be written down -- that's what writing is for; ergo, it always has the potential to exist in written form and when somebody does write it, there it is. On the other hand, I hold fast to the notion that there is never more than one apostrophe in a word. Notwithstanding that there are two elisions in the present case, I would suppress one and spell it "I'dve".