Hey Hey Hey! I *think* for that update the only category you would need to add is the "bludgeoning & piercing". However, the halberd`s Swiss army knife-like versatility, allows the choice using the spear point to do the "piercing", and the axe blade to do the "slashing"... and the hook has its own tripping rules. I don't know if that is more or less difficult to implement or even worth it for a single weapon.
I feel a little awkward imposing a massive workload for you ..