I think most of these lyrics are well crafted, and I'd agree with the points about "memory police" not being developed enough to be the hook.
What came to my mind is the possibility that the real police -- and likely alcohol -- could have had something to do with why his marriage ended. If he blames himself for what happened, the "memory police" could be a symbol for holding on to that guilt.

Anyway, it seems like a stretch.

And I know that sometimes you have to suspend a little disbelief for a story, but the idea that a shellshocked alcoholic is going to make a living as a "freelance" artist just doesn't ring true. (Honestly, I'm not sure what you mean by a freelance artist.)OK, I'm sitting here drunk staring at my brushes, but now I'm going to get up and paint some client's beautiful rose garden or this little girl's portrait.

Since he's in that big house, maybe he could be going from room to room painting what he remembers of her on the walls when he's not drinking to forget her. Hmmmm. That could make a good short story.