She could've just done this from the beginning instead of forbidding her clerks from doing so and causing a scene, but okay, it's always the liberals' fault in your world when it comes to LGBT rights.
Yes, she could have tried this from the beginning and taken things into her own hands in this way rather than the way she did, the questionable legality of such an action without explicit approval would still exist. The judge could also have put this forward as a solution, but he didn't. The Governor and the legislature could have seen this coming and put forward a way to resolve these disputes, but they didn't. My criticism of liberalism here is just that it identifies this dysfunctional mess as a moral imperative so that the jailing of the 'witch' (she fills that archetype here) in itself represents some sort of progress, since to do otherwise would be to admit that non-liberals, whatever their personal or political faults, might have a modicum of a legitimate interest to consider. Gay rights activists have of course not created this approach to the law which exalts the adversarial and excludes the mediational when it comes to social controversy; they have merely extended it.