I think in the absence of a proposed method we must consider as undemonstrated the claim that information can be ordered without defining how it is quantified.
Yup. And we must consider as undemonstrated that information must be quantified to order it. We don't even know if information as any particular creationist conceives it can be ordered or quantified. All we can know is that, in order to meaningfully claim that some process has or has not increased information, that information must be quantified and/or ordered.
That final step is, of course, the step that few creationists even attempt. And those that do attempt it unfailingly end up with someone else demonstrating a process that does increase that particular creationist's version of information.
My only real point here is that "you must quantify information in order to claim it has or has not increased" is not true. "You must quantify or order information in order to claim it has or has not increased" is true.