It is a "not...or." "Not...ors" in English are ambiguous, even though, in mathematics, through syntax, they can be rendered unambiguous.
The law, to me (and likely to the courts) says that refusal of any one of the three violates the law. The words, “no person...shall refuse to disclose the person’s name, address, or date of birth," can be logically equated to, "no person shall refuse to disclose the person's name or shall refuse to disclose the person's address, or refuse to disclose the person's date of birth," or to, "no person shall refuse to disclose the person's name or shall refuse to disclose the person's address, or refuse to disclose the person's date of birth," making any one of the actions an offense. Of course for there to be a refusal, there must be a demand. You need only give what the officer lawfully demands.
Caveat: It is impossible to know for sure that an officer does not have RAS. It may be a lie, but if someone calls and says that you were handling the firearm while arguing loudly with someone, he may well have RAS. So, if you assume he does not, and refuse to identify yourself, you could be committing a crime. I'd consider asking the officer directly, recording his answer, of course: "When you demand that I identify myself, are your making that demand because you are detaining me under the conditions listed ORC §2921.29(A)? If you are, I will comply. If not, I am not required to do so," or something like that. If he refuses to answer, I'll have to assume, for my own legal safety, that the demand is lawful and will answer. However, he will have to answer for his actions too. Both sides of the conversation will have been recorded for posterity.