I definitely agree with your disinterest in HP. It's something I've been exploring doing away with for a while — my other project, Fate/Last Chance, has no HP at all, replacing it with an abstracted "battle tension" system to increase the same action-feel I think you're searching for. We made the choice to embrace HP and the grid in Blades of Ether on purpose, though; our goal is for the grid tactics feel to encourage partner and party cooperation in the moment to moment of battle.
I'd be very interested to hear what changes you implement and how they work out! If you hit on something really fun, it very well could become a rulebook adjustment.