Great question Ambayard!
I've dealt with (monster) HP in a few ways. When I first starting playing Apoc D&D, I was using an abridged version of AW, with 'wounds' in an hourglass. I discarded this system once HP became hard-coded by Sage and Adam. It just felt measurable and more 'D&D'.
Since though, I've come to the conclusion that when I GM, I like to have a rough idea of the monster's HP as a measure of its 'toughness', but also as a pacing mechanism. When we use Hack and Slash (or any move for that matter), the temporal scale can shift as the fiction demands. Not all melee is blow for blow, sometimes it is a whole exchange in one move.
In this sense, Sage's insight into HP being a measure of 'mistake potential', rather than 'health', set of a bell in my head. Simultaneously, I've digested a few commentaries by D&D contributors on the evolution of HP (from OD&D to 4e), elucidating this mechanical gem. So now, for me, HP are an ablative measure of narrative pace. They invoke a sense of trepidation as they lower; monsters and characters are fully functional and healthy, but the tension is ramped up with the emminent fear of death.
To that end, I have a huge stack of counters that I give to each player representing their HP. This then becomes a visual cue to me (and them) on how many 'mistakes' they have left. It also is a gauge for me as to whether I want to make the hard move of dealing damage. If the fiction is a little 'meh' and I have the opportunity to deal some damage, then whittling down this 'mistake potential' resource is a simple and direct way way of focusing the story. Its just another way of using up their resources.
Monsters? Well, I do tend to track their HP too, using the same counter measurement. When the players first deal damage, I allocate a number of HP tokens in plain view, either straight from the monster stat block, or a 'by feel' allocation. If the players are willing to take on a hugely more challenging encounter, despite all of my grim portents, well so be it. Then the players can deal damage as they see fit through their moves. This gives them an idea of how close they are to fictionally overcoming this monster 'challenge'.
I also have been playing with the concept of ablating a monster's HP through means other than Hack and Slash or Volley or Spells. This may neutralise the monster completely and the pile of tokens is removed as the monster effectively 'exits' the scene. This may be its death or subdual, but often it may be a hasty retreat or a successful Parley or even a change of heart.
So when HP tokens are 'on the table' its a cue to the group that the fiction has potentially become life and death. There are serious ramifications. The monsters are willing to fight for what they believe in (their instinct) and are present, available for the PC's to interact with fictionally. The new bonds reward cycle ties in nicely with this goal-based XP, and I can cater the monsters as suitable obstacles that I think will enhance the emergent story based on these player flags. Helps me, helps them :)