There's always magic.
Batman might not be able to help with that, but he knows a few who could.
I really don't know what would come from such a storyline. I
like secret identities. But several have operated with known identities with no significant problems. I expect, as others have stated, the biggest blowback would be on Jim. I was also going to say that no one would buy him not knowing the identities of Batman and the others, but I'm not really sure was the current continuity is on how tied Batgirl is (was in the past) to the rest of them in the public eye.