Many thanks for the responses. The counsellor stopped by today on his way home from training and we had a cup of tea. (AH was upstairs sleeping but counsellor said that's okay, he just wanted to talk with me.)
Counsellor explained to me that he has been trying to get AH to take some responsibility towards reducing or at least recording intake before detox could happen--but mostly he wanted to have some sort of plan in place for AFTER detox and explained that he and AH needed to have some idea of what that plan would look like before they could proceed. It couldn't be like, let's bung you into medically supervised detox with no plan for afterwards. Otherwise, in his experience, he'll be in detox again the next month.
That said, he was concerned about the medical symptoms I described and explained that the results from the liver function test would be going straight to a GP at the substance abuse clinic--which I hadn't appreciated--and that if they showed a significant problem they would just put him in detox right away to address health problem concurrently.
Also, it turns out that AH was given the info to go get the liver function test two weeks ago.
I did get my oar in about these requirements that AH's been given, how they seemed to presuppose a certain level of cognitive function, and how the liver function stuff didn't get addressed until I barged in. He seemed to hear me and take that on board.
He did mention that "the three of us" could work together to help the problem--which, hmm. On one hand, yeah, he's my AH, but on the other hand... well, you know. I already have a job and, you know, a being, outside of AH's alcoholism.
But I do feel a bit better about the whole situation. It's really helped to vent here, thanks.